I'd imagine so, yes, before being pushed back to the edges and corners of the islands. Shame the warrior culture took over a less militarily focused one. History rhymes, no?
Of course its speculation from my side but it wouldn't be surprising if it was related to the Romans effectively "demilitarizing" the local society to reduce the likelihood of rebellions and general civil unrest.
That might have worked fine enough as long you had a professional army guarding the borders but when that army was gone everyone was effectively left defenceless.
Something like that seemed to have happening in Spain and Gaul as well. Except unlike in Britain the local populations managed to somewhat assimilate their Germanic overlords.