"I'm not sure that there's any proof that all the celtic languages in Britain were from the Brythonic (or p) branch of celtic"

To be fair to David though he was talking about the Roman occupation so rather than Britain as a whole we are really only talking Roman Britannia which is England, Wales and perhaps southern Scotland. Do you know of any Celtic languages which were non Brythonic in this area during Roman times? Perhaps the Irish invaders in wales at the end of the Roman period but that is hardly an indiginous (for want of a better word)language surviving!

You are right in that some regard the different strains of British (ie Welsh, Cornish, Cumbric) as being dialects whilst others regard them as sister languages.

Outwith Roman Britannia proper Scottish historians have been pretty settled for some time now on the main Celtic language of the Picts being Brythonic too - prior to them later being Gaelicised. By tradition the Gaels arrived in Scottish Dalriada around 500AD with King Fergus so that of course post-dates Roman times anyway. However again historians now seem to concede that it was simply a change of power base and that the Gaels must have been in Dalriada prior to that. Some claim that the Epidii tribe of Roman times were already Gaelic speaking. In truth we don't know for sure.