The loss of apostolicity was not confirmed till much later:
It was natural that this advance section of the Anglican Church [i.e. the leaders of the Anglican Revival] should seek to ratify its position, and to escape from its fatal isolation, by desiring some scheme of corporate reunion and especially by endeavouring to obtain some recognition of the validity of its orders. With the truest charity, which consists in the candour of truth, Pope Leo XIII in his Encyclical on Unity, pointed out that there can be no reunion expect on the solid basis of dogmatic unity and submission to the divinely instituted authority of the Apostolic See. In September, 1896, after a full and exhaustive inquiry, he issued a Bull declaring Anglican Orders to be "utterly null and void", and in a subsequent Brief addressed to the Archbishop of Paris, he required all Catholics to accept this judgment as "fixed, settled, and irrevocable" (firmum, ratum et irrevocabile).(Anglicanism )
Finally, with apologies for the long quote, this is a chapter in the Catholic Encyclopedia that deals with the reasons the separation was formalized:
THE BULL OF LEO XIII
From the foregoing account it can readily be understood why the practice of re-ordaining convert clergymen has subsisted. Anglicans, however, have always resented this practice, and maintained that the Holy See could never have sanctioned it had the facts been properly presented.
In 1894 this contention was pressed upon the notice of some French ecclesiastics by some Anglican leaders who were discussing with them the prospects of corporate reunion. The result was that the French ecclesiastics brought the matter to the notice of Leo XIII, assuring him that this impression prevailed among many well-disposed Anglicans, who felt that they were being unfairly treated. The Pope was moved by what he heard, and determined that he would have the whole question re-investigated thoroughly. Accordingly, he selected eight divines who had made a special study of the subject, and of whom four were known to be disposed to recognize Anglican orders and four to be disposed to reject them. These he summoned to Rome and formed into a consultative commission under the presidency of Cardinal Mazzella. They were given access to all documents from the archives of the Vatican and the Holy Office which would throw light upon the points at issue, and they were bidden to sift the evidence on either side with all possible fulness and care. After sessions which lasted six weeks, the Commission was dissolved, and the acta of its discussions were laid before a judicial committee of cardinals. These, after a two months' study, in a special meeting under the presidency of the Pope, decided by a unanimous vote that Anglican orders were certainly invalid.
After an interval for prayerful consideration of this vote, Leo XIII determined to adopt it and accordingly published his Bull "Apostolicae Curae" on the 18th of September, 1896. In this Bull he begins by expressing his affectionate interest in the English people and his desire for their return to unity, and by reciting the circumstances which had led to the issue of this solemn decision. He then calls attention to the action taken in the same matter by his predecessors.
In the reign of Mary, when she and Cardinal Pole were engaged in reconciling the kingdom, letters of direction were sent to the latter, which, as their text shows, required him to treat those who had received orders by a form other than "the accustomed form of the Church" — a phrase which, says Pope Leo, can only refer to the Edwardine Ordinal — as needing to be ordained or consecrated afresh. At that time, then, the Holy See judged the Anglican form to be insufficient, and that it persisted in this adverse judgment is manifest from the fact that for more than three centuries it has sanctioned the practice of re-ordaining absolutely the holders of orders obtained through this form; for "since in the Church it has always been a firm and established rule that the sacrament of Order ought not to be repeated, it never could have silently acquiesced in and tolerated such a custom", had it deemed the Anglican form to be in any way sufficient.
Moreover, continues the Bull, the Holy See not only acquiesced in the practice, but on many occasions gave it renewed sanction by express judgments, to two of which, the second being that of John Clement Gordon, it calls particular attention, repudiating in connection with this latter the allegation that the rejection of Gordon's previous orders had been motivated by any other cause than the character of the Anglican rite (a copy of which was procured and examined by the judges), or even that in judging of the rite the essential point considered was the omission in it of any tradition of the instruments.
This account of the practice of his predecessors forms the first part of the "Apostolicae Curae", and in view of it Leo XIII observes that the question could not really be considered still open. He has wished, however, "to help men of good will by showing them the greatest consideration and charity," and he proceeds to expound the principles on which the Anglican Rite is judged by himself, as well as by his predecessors, to lack the conditions of validity.
"In the examination", he says, "of any rite for the effecting and administering of Sacraments, distinction is rightly made between the part which is ceremonial and that which is essential, usually called the "matter" and "form". All know that the Sacraments of the New Law, as sensible and efficient signs of invisible grace, ought both to signify the grace which they effect, and effect the grace which they signify. Although the signification ought to be found in the whole essential rite, that is to say, in the "matter" and "form", it still pertains chiefly to the "form"; since the "matter" is the part which is not determined by itself, but which is determined by the "form". And this appears still more clearly in the Sacrament of Orders, the matter of which, in so far as we have to consider it in this case, is the imposition of hands, which indeed by itself signifies nothing definite, and is equally used for several orders and for confirmation. But the words which until recently were commonly held by Anglicans to constitute the proper form of priestly ordination — namely: "Receive the Holy Ghost" — certainly do not in the least definitely express the sacred Order of Priesthood, or its grace and power, which is chiefly the power "of consecrating and of offering the true Body and Blood of the Lord" (Council of Trent, Sess. XXIII, de Sacr. Ord., Can. 1) in that sacrifice which is "no nude commemoration of the sacrifice of the Cross" (ibid., Sess. XXIII, de Sacr. Miss., Can. 3) . . . . The same holds good of episcopal consecration. For to the formula, "Receive the Holy Ghost", not only were the words "for the office and work of a bishop" etc., added at a later period, but even these, as we shall presently state, must be understood in a sense different from that which they bear in the Catholic rite."
In this passage the Bull sanctions the principle that a sacramental rite must signify definitely what it is to effect, and that this definite signification must be in the essential "form", or words in proximate connection with the "matter"; also that, in the case of Holy Order, what must be definitely signified is, in the ordination of priests, the Order of the Priesthood or its grace and power, and similarly in the consecration of bishops; the grace and power in each having reference to the accomplishment of the Holy Sacrifice of the Mass.
This principle accepted, it follows at once that the Anglican Ordinal, at least as it stood till 1662, lacks the essential conditions of sufficiency. But the Bull further examines how far the remainder of this Ordinal, or the circumstances under which it came into being, can be held to determine the ambiguity of the "essential form". And here it sanctions the judgment which the Catholic writers had already formed. "The history," it says, "of that time is sufficiently eloquent as to the animus of the authors of the Ordinal against the Catholic Church; as to the abettors whom they associated with themselves from heterodox sects; and as to the end in view . . . . Under a pretext of returning to the primitive form, they corrupted the liturgical order in many ways to suit the errors of the Reformers. For this reason, in the whole Ordinal not only is there no clear mention of the sacrifice, but every trace of these things which had been in such prayers of the Catholic rite as they had not entirely rejected, was deliberately removed and struck out. In this way the native character — or spirit, as it is called — of the Ordinal clearly manifests itself. Hence, if, vitiated in its origin, it was wholly insufficient to confer orders, it was impossible that in the course of time it should become sufficient, since it remained always what it was (i.e. of vitiated origin) . . . . For once a new rite has been initiated, in which, as we have seen, the Sacrament of Orders is adulterated or denied, and from which all idea of consecration and sacrifice has been rejected, the formula, "Receive the Holy Spirit" (the Spirit, namely, which is infused into the soul with the grace of the Sacrament) no longer holds good, and so the words "for the office and work of a priest or bishop", and the like, no longer hold good, but remain as words without the reality which Christ instituted."
Likewise in regard to the defect of intention, the Bull endorses the judgment adverse to Anglican ordination which Catholic writers had always urged. "When anyone has rightly and seriously made use of the due "form" and "matter" requisite for effecting or conferring the sacrament, he is considered by that very fact to do what the Church does. On this principle rests the doctrine that a sacrament is truly conferred by the ministry of one who is a heretic or unbaptized, provided the Catholic rite be employed. On the other hand, if the rite be changed, with the manifest intention of introducing another rite not approved by the Church, and of rejecting what the Church does, and what, by the institution of Christ, belongs to the nature of a sacrament, then it is clear that not only is the necessary intention wanting to the sacrament, but that the intention is adverse to, and destructive of, the sacrament."
These are the defects in the Anglican Succession, on the existence of which the Bull bases its decision. It will be noticed that they are of the most fundamental kind, and are independent of any defects that may be thought to arise out of the omission in the Ordinal of a tradition of the instruments, or of the doubt about Barlow's consecration. To examine into the nature and bearing of the latter when a sufficient basis for a certain conclusion had been supplied by the former would have been a superfluous task, and for the same reason it is unlikely that even for the private inquirer these other considerations will retain in the future the interest they had in the past. At the same time the Bull has in no way pronounced them to be frivolous or unfounded, as has been suggested. It remains to give the formal definition of the Bull, which is in the following terms: "Wherefore, strictly adhering in this matter to the decrees of the Pontiffs Our Predecessors, and confirming them most fully, and, as it were, renewing them by Our authority, of Our own motion and certain knowledge We pronounce and declare that ordinations carried out according to the Anglican rite have been and are absolutely null and void."
The publication of the "Apostolicae Curae" caused, as was to be expected, much excitement in England; nor did the Anglican party, for whose sake it was intended, show any disposition to accept either its arguments or its decision. It was deemed, however, to have created a crisis sufficiently serious to require that it should be met by some formal reply. Accordingly, in the early part of 1897 there appeared, in both a Latin and an English edition, an "Answer of the Archbishops of England to the Apostolic Letter of Pope Leo XIII on English Ordinations", which was "addressed to the whole body of Bishops of the Catholic Church". This answer, which came to be known by its Latin name of the "Responsio", is a distinctly Low-Church document, of which the leading contention is that the Pope has misjudged the Anglican Ordinal through failure to recognize the right of national Churches to reform and revise their own formulas, and by applying to this Ordinal a false and untrustworthy rule. The true rule to which an ordinal should be conformed, it urges, is the rule of Holy Scripture, and it is in this rule that the Reformers sought their guidance. They found an enormous accretion of sacerdotalist ideas embodied in the words and ceremonies of the older Ordinal, whereas, in the New Testament, the sacerdotalist conception of the Christian ministry was altogether absent. And, on the other hand, they found that the aspects of the Christian ministry on which Our Lord and His Apostles had laid the most stress — those, namely, which concerned the pastor's duty to go forth in His Master's name as His steward, His watchman, His messenger, to tend the sheep, and, if need be, lay down his life for their sakes, to preach the word, to convert sinners, to remit offences in the Church, to render mutual services to one another, and much else of the same kind — were very insufficiently set forth in the Pontifical. Accordingly, in drawing up their new rite, they endeavoured as far as possible to eliminate the former element and give prominence to the latter, while in their "forms" they assigned to the priesthood the words which, according to the New Testament, Our Lord used in promoting His Apostles to this office, and to the episcopate the words of St. Paul which "were believed to refer to the consecration of St. Timothy to be Bishop of Ephesus". Nor, in following precedents so lofty, could they reasonably be charged with having endangered the efficacy of their rite. This is in brief the defensive argument of the "Responsio". But it also charges the Pope with having, in his zeal to condemn the orders of the Anglican Church, overlooked the contradictions in which he was involving the position of his own Church. In condemning the Anglican "forms" as wanting in definite signification, he condemned, by implication, the orders of his own Church, since the Roman Pontifical in its pre-medieval text was not a whit more definite than the Elizabethan Anglican; and in attaching the sacramental virtue to the imposition of hands and the connected words he was condemning by implication his predecessor, Eugenius IV, who attached that virtue to the tradition of instruments and the words connected therewith, not even making mention of imposition of hands among the requisites. One thing was made clear by the "Responsio", and by the other criticisms of the "Apostolicae Curae" which poured forth from the Anglican press, namely, that the character of the Bull and its arguments had been greatly misapprehended. Hence, Cardinal Vaughan and the English Catholic Bishops, in the early part of 1898, published a "Vindication of the Bull 'Apostolicae Curae'", in reply to a letter addressed to them by the Anglican Archbishops of Canterbury and York." In this "Vindication", after some preliminary observations on the extrinsic reasons which the Bull had given for its decision, attention is called to the false standpoint from which the two Archbishops had judged the arguments of the Bull. In their "Responsio" they are mainly occupied with challenging the soundness of the principles on which the papal decision had been based. They urge that it rests on a false and unscriptural conception of the priesthood, and that, if for this the more scriptural conception expounded by themselves had been substituted, the decision must have been different. But this, the "Vindication" points out, is ignoratio elenchi. Of course the Pope considers that the Catholic conception of the priesthood is in conformity with Scripture; but that was not the question under consideration. The Anglican grievance was that those of their clergy who came over to us were re-ordained; and to complain of this was to contend that even on our principles their orders ought to be recognized; while no doubt the particular section of the Anglican communion which took most to heart this practice of re-ordination was in substantial agreement with us as to our conception of the priesthood. Hence the Holy See, in examining the question, necessarily assumed the validity of its own principles, and inquired only if they had been duly applied. The "Vindication", however, to facilitate the understanding of the Pope's reasons, sets itself to expand, explain, and vindicate by reference to the facts those points which the Bull, after the manner of legal documents, gives only in a highly condensed form. It is not necessary here to epitomize the "Vindication", but mention may be made of its study of the opinions in regard to the Eucharistic Presence, the Mass, and the priesthood of Cranmer and his associates, as likewise of the opinions on the same subjects expressed by a series of Anglican divines during the sixteenth and seventeenth centuries, which showed that the tradition initiated by Cranmer persisted.
(Anglican Orders; the links will work at source).