Those advocating swift surgery are assuming that it's just a matter of cancelling a national treaty. If only it were so easy. But the ties linking us to the EU are intricate, long-established and at many different levels: not just national but regional, local, business-to-business and personal. For them to be peremptorily severed without planned alternatives would cause a great deal of pain, especially to our own citizens: and risk alienating the individual member countries and citizens of the EU which we have every reason to retain as friends, and much to lose by making enemies.
It could be done quickly if there were a carefully prepared contingency plan in place in which all the necessary microsurgery is anticipated. But there isn't, presumably because nobody who might have prepared such a plan believed before the referendum that it could turn out as it did. In its absence, it's got to be done slowly and carefully, with proper parliamentary oversight, if those negative outcomes are to be avoided.