Roman Britain was somewhat of an exception, compared to other areas in the Roman Empire. Firstly, Roman Britain was an outpost in the Empire and it really did not attract massive settlement, as other parts of the Empire did.

As a result, Latin did not take over as the main language as it did in most places in the Western Roman Empire and in Dacia.

What existed in Roman Britain was a 'dual' language society. The Romans kept speaking their Latin, but the native Britons kept speaking their own dialects -- from which we have modern day Welsh. The Romans were in modern day England for four hundred years and during this time there was this 'dual' society.

When the Romans left Britain (due to Roman downsizing), there was no more need to use the Roman Latin language and it was quickly forgotten. Only a few words were borrowed from Latin into the Briton language (which we call 'Welsh' nowadays).

After the Romans left, the Anglo-Saxon settlement began. In this 'invasion', we see the modest origins of the English language. And we see the original Briton language being pushed out, assimilated or pushed into Wales.

For more pre-Anglo-Saxon linguistic history, I would recommend Bill Bryson's book, Mother Tongue.