Paladin, your argument is only historically correct in the sense that its the same church because its in the same nation. You might as well argue that the Lutheran churches are the same as the roman catholic churches which were in those localities prior to the reformation.
The anglican church during and after Henry VIII was not simply a return to the ancient traditions of the pre Norman church. The Anglican church can trace its roots back, especially because of Apostolic succession.. However, like it or not, the Anglican tradition as it exists today can not realisticly be said to have existed prior to Henry VIII. The best you could possibly say is that the Anglican tradition born after Henry VIII retained many elements from the earlier tradition(s). Anglicanism may have retained its catholicism and its orthodoxy, but it can not be denied that the anglican tradition was created as a result of mixing in a good deal of "reformation" thought. In fact, for the first 300 years or so of the "anglican tradition" it had alot more protestant influence than it even does today.
A note on the celtic church. Very little reliable information exists today on what the celtic church taught and practiced. The celtic church was almost destroyed, not by Roman influence, but by barbarian conquest. The celtic church pretty much ceased to exist in most of "england" because it had been over run by pagan saxons and angles.. not roman missionaries

When Augustine arrived he found very little in the way of an active church among the saxon's etc. Thus he was not so much going to bring the celtic church into line, as to evangelize the pagan tribes that had settled in southern england. At roughly the same time there was a resurgance of celtic christianity in the north with the influence of the Lindisfarne community and so on. The two churches eventually met in the middle and when their divergent practices came into conflict the council of whitby was held to resolve the differences.
It is interesting that the only major issue addressed at Whitby was a calendar issue, the method by which easter should be calculated. There are comments by some of the Roman people of the time about the celtic liturgy being backwards or barbaric in terms of language, but no indication that it had any significant difference in theology or doctrine. Thus there is no particular reason to assume there was ever a great conflict between celtic and roman churches over anything but the calendar.
There have been alot of theories about pelagian vs. anti pelagian doctrines being a difference, but there is little or no historical evidence that I've ever been able to find that lends real proof to any of that.