Cultural domination and apartheid.
The only parts of England that are more 'Anglo Saxon' than the rest are the east and south east, the English are mainly descended from the Briton tribes that were in England.
Language can be very easily destroyed, Wales and Cornwall at one point nearly stopped speaking their Celtic languages completely, but a celtic revival helped boost them back, it is no wonder that an army of Germanic invaders could easily force their way of life onto them.
You might already have seen the DNA results and analysis from England proving similar genetics to the Welsh, but back to the language...
Well, there are indeed some parts of England that clearly have celtic language history - there was evidence of a Devon (Dewdansek) Cornish (Kernow) and even a Cumbrian langauge (Cumbria is a large county in the North of England).
There is also complete lack of Archaelogical evidence for mass ethnic cleansing from the Anglo Saxons, it is expected that 2 million Britons would be slaughtered, however - no documents, no mass burial grounds, no nothing.
Bear in mind that English is a language that has been heavily 'Latinised', and also has various Viking origin words, indeed if you went back 1100 years and tried to speak modern English to the inhabitats at the time, you and they would not understand a word one another was speaking.
Ireland Scotland and Wales were never heavily invaded by Germanic tribes, although it is clear that some Irish settlement names and words have some norse orgin.
As for Scotland - there was a point that Scottich gaelic was almost a lost language but thakfully never truly died out.
The reason why England could not try to revive their old celtic language is because they would have no idea what it would have sounded like, in honesty, Welsh probably sounds nothing like what the celtic tribes would have spoken, various Celtic (Brythonik) tribes spoke several various dialects of the language, there is even more reason to believe this because of the difference (and similarities of course) between Cumbric, Devonian Cornish and Welsh. You may also see that Gaelic and Brythonik are completely miles apart in terms of language structure.