The point was made, I believe, in your initial query that asked about the antiquity of 'paedobaptism': that it is important to distinguish between two parts of the single baptismal issue. Namely, the
look of some practice, and it's
significance.
There were Christian-elements during the patristic church-era that would inevitably have practiced something like 'credobaptism,' inasmuch as they
delayed baptism for as long as they dared, in order to maximize it's supposed benefits. If you could be baptized on your deathbed, you would pretty much wash away a lifetime of sins: from the stain of original sin, to the sins prior to saving faith, to the sins after claiming Christ as Lord and Savior.
Then, there's the practice no one doubts: that converts from the beginning were regularly baptized either upon initial conversion, or after a period of catechizing in the content of the faith. In either of these cases, the practice of infant baptism is largely sidelined. The
practice in view is concerned with bringing in professors to church membership and privilege. Baptism is supposed to relate to that, somehow.
And yet, as the example of delayed baptism demonstrates, the underlying issue is the understood
significance of the practice. What did folks intend by what they did, and was this intention in accord with the apostolic doctrine? How far was it removed? It is somewhat anachronistic to use the early church to defend the Reformation era's theology of baptism among the Protestants; and then assert that the English Baptists have no recourse to the same body of history, if they choose to refer to elements of it as rather supportive of certain contentions they make.
The issue is further complicated by two items of historical note. One is the occasional bit of knowledge we retain of baptismal (or similar) practices of various fringe or heretical groups from ancient through medieval periods. It doesn't help things, that some modern Baptist historians have latched onto "anything non-Roman" as evidence of the persistence of true faith and practice outside the Roman institutional church where all evils were housed. The Albigenses/Cathari for instance have been appealed to as proto-Baptist, mainly (it is reasoned) because Rome must have persecuted them because of their good faith and practice (there being no other possible motive?).
Second, the Anabaptist movement that arose in parallel to the Reformation (esp. Lutheran/Reformed/Anglican) produced an entire third stream of history of about 500yrs old today. The Anabaptist theology and practice of baptism is the real "new to the late era" baptism. The first purveyors of the Radical reformation were not embarrassed to proclaim they were resurrecting the (supposed) apostolic practices, which were essentially lost for 1500yrs. Again, one must draw the distinction between their employment of some form of baptismal
practice, and the
significance which they imputed to it.
That said, the truth is that the Anabaptist approach has exerted definite influence upon a whole swath of the modern 'evangelical' church. Such that, the modern justification for baptism in that vaguely defined conglomeration of Christian-groups is largely borrowed from the Anabaptists, not the ancient church, not Rome (of course), and not the Reformers.
It is the case, that one may trace some baptismal affinities in the English Baptist movement to influences from the continental Anabaptists.
http://www.history.ac.uk/reviews/review/557 The Isles were far from hermetically sealed off from Europe. John Smyth was an Englishman gone to Amsterdam, influenced by Mennonite (Anabaptist) sects there, and set up possibly the first English Baptist church there in 1609. He self-baptized, though not by immersion. His group eventually split between those who joined the Mennonites, and those who returned to England, setting up the first church of record (first one we can affirm historically) in London in about 1616.
This page
http://www.reformedreader.org/history/bryan/ch03.htm rebuts the idea of lineal descent of English Baptists from the continental Anabaptists (the whole paper is worth reading in conjunction with this question). The author means to show that in the principal or core issues of the faith, the doctrine of the English Baptists was not a product of the Radical reformation, but of the Reformers. This is undoubtedly true. And yet, it remains true that what is proved supports the idea that the credobaptism of the Baptists is essentially
restorationist. Purification of baptism, it is said, required the elimination of subjecting infants to the rite. There is far less continuity, in this view, to the habit of the church through the intervening centuries.