The Normans didn't tear down every Anglo-Saxon church, there's still a number of them standing. A surprisingly high number given their age, really.

https://en.wikipedia.org/wiki/Category:Standing_Anglo-Saxon_...

Thanks, wouldn't have guessed to search for that list. In the entry for Escomb Church, is says there are "only four complete Anglo-Saxon churches remaining in England, the others being St Lawrence's Church, Bradford-on-Avon, Greensted Church and All Saints' Church, Brixworth."

Looking through the list, it seems that in the Anglo-Saxon portions of all those buildings, any arches were relatively narrow and crudely fashioned compared to subsequent Norman style. So I guess there was quite a gap in sophistication of architectural knowledge between Britain and the Continent in the 11th century.

Yeah, the Anglo-Saxon period was a time of a much less sophisticated building techniques, the UK was an early loss from the Western Rome and the sophistication of the material culture under the Anglo-Saxons there was grim. The Romanesque style of the Normans was largely a continuation and development of late Imperial Roman building traditions (loaded with deliberate callbacks) that grew very sophisticated. That part of the continent had hung onto more of the late Roman engineering traditions that were lost in Britain, so they were able to produce much larger, more impressive buildings, and they had a much richer cultural vocabulary in their iconography and art of their churches as well.

If you are interested in the story of the Norman reconstruction of institutional architecture in England, there is a quick overview in Garnett's The Norman Conquest: A Very Short Introduction. (https://www.goodreads.com/en/book/show/5056609-the-norman-co...)

From the book:

...within fifty years of 1066 every English cathedral church and most major abbeys had been razed to the ground, and rebuilt in a new continental style, known to architects as 'Romanesque'. (p. 10)

...No English cathedral retains any masonry above ground which dates from before the Conquest. (p. 11)

...Old England, in an architectural sense, had been eradicated. (p. 12)