I've never come across this theory, and I don't give it much credence. Even if there was no large scale migration to Britain, there absolutely was an Anglo-Saxon invasion that at least affected the upper classes/rulers & warriors. After that there was probably heavy anglicisation of local Brittonic celts, but the idea that they'd adopt an entire language and culture because of trade and admiration alone seems weird. Likely however there was more large migration than previously thought, not less.