After Paul's first imprisonment I believe he traveled to Spain...and then on to England before returning to Asia Minor. There is a gap between the two imprisonments and scripture does speak of him wanting to go to Spain [Romans 15:24 and Romans 15:28]. We know that his first visit to Rome was in custody so it is reasonable to believe he went on to Spain after being released. The "Sonnini Manuscript" tells of Paul's visit to Britain and Spain. This would have been the only time to accomplish this journey and I believe would have left him little time to meet Simon Peter in Rome.
This Sonnini Manuscript means therefore that Peter and Paul could never have been together in Rome preaching as Irenaeus and Ignatius state, leaving us with the conclusion that they were either mistaken, or two fellows "called Peter and Paul", were together in Rome.
According to Irenaeus, Simon Magus had a companion who was also from Samaria, known as Menander, a fellow practitioner of magic. As Magus was called "Peter", Menander may have been called "Paul".
Note here the beginning of a tradition of the Roman religion descended from Simon Magus, where upon becoming head Bishop, the head Bishop assumes a saintly pseudonym and is called by that saintly pseudonym.
Furthermore, according to Irenaeus, the successor of Simon Magus was Menander. It is entirely possible that upon succeeding to the sacerdotal chair of Simon [Peter] Magus upon his death under Nero, that Menander chose the pseudonym "Linus", and thus the descent of the Papacy through a person "called Linus".
Finally, the most incredible revelation of Irenaeus thus far is that the ninth bishop in succession from Linus, was Cerdo, a follower of the doctrine of Simon Magus. That would make him the one "called Pius I". Then succeeding Cerdo [Pius I] was none other than the infamous Marcion, the 10th Bishop from the one "called Linus". That means that Marcion, one of the most dangerous heretics of all time, the greatest single propagator of the heresies of Simon Magus in the Ante-Nicene Church, was none other than the one that Roman Catholic faithful revere as Pope Anicetus.
If only they read their Ante-Nicene Fathers and quit listening to their Magisterium, they would know these things.