Celtic counting rhymes were used in England for centuries after its Anglicization. How long were Brythonic languages spoken in England after the establishment of Anglo-Saxon power?

One of the curiosities about the AS period is that the language took over so quickly and so thoroughly. By about 570AD English is spoken pretty much everywhere, having successfully driven out Latin and Brittonic languages. The problem is determining how it did this, and how do we know this.

Lacking any pre-600AD documentation in almost any language means we have to figure it out through multiple avenues. The linguistic argument is that Latin and Brittonic were substrate languages to Anglo-Saxon, which was a prestige (superstrate) language. Substrate speakers become more fluent in superstrate languages quicker than superstrate speakers becoming fluent in substrate languages, so Latin and Celtic speakers adopt Anglo-Saxon better than Anglo-Saxons adopt Latin and Celtic - this is the linguistic model, and it works in Anglo-Saxon England. Superstrate languages have very low uptake of substrate languages: Old English has very few Brittonic loanwords, so it nicely proves the linguistic model.

Another primary method is place-names. Place names during the Roman period tend to be Latinised versions of Brittonic names, which were generally about geographical features, so lots of names incorporating rivers/hills/fortresses- (these have the highest survival rate in AS times.) Camulodunum is simply Camalus+dunon => Camulodunum. Exeter = Isca Dumnoniorum ('Isca of the Dumnones'). We only know about 250 Latinised Celtic names. Almost every one of them was replaced by an Anglo-Saxon name, and there's no authoritative reason why - immigration or invasion have been mooted as reasons why - Celtic place names survive in the west of Britain, Anglo-Saxon ones in the east, but even this isn't complete - Wales generally has a large number of Celtic names, but the majority are still in Anglo-Saxon. In some cases, the later writers didn't know their Latin - Portsmouth is named after a man called Ports according to the Anglo-Saxon Chronicle s.a. 501, when the original Latin (port - to carry) has been forgotten.

You could get technical about Celtic languages, and say they were spoken for a long time after the Anglo-Saxons. Bede, by 731, distinguished Anglo-Saxons from Britons based on their language, so you could argue that there were still elements alive by then. The last native Cornish speaker died in 1777, the last native Manx speaker in 1974, but this is largely against the trend.

There are very few modern celtic words still in use: my favourite possibility is crumpet, from the Breton, krampoez and I've read as little as 20 words still remain in common parlance. Place names are the best place to find them.

Edit: added map, from Higham's Anglo-Saxon World

I feel that I should reply to this article by pointing out that they are still in use, at least among some older people in very rural areas, and it will only be with the death of that generation that they will finally go out of use. I think it's the wrong question to ask how long Brittonic languages were spoken in connection with this. The point of rhythmic counting is that it was accessible to people who were not numerate. I think you will find that it has survived among people with limited or no access to education. There was no equivalent in the Anglo-Saxon language, and so the Brittonic versions stayed in use. I would not take that as an indication that Brittonic languages were still in use, but rather that the vast majority of the rural population in areas where these were used were not numerate.