Did you know that ALL of what is now england and even part of southern scotland was entirely welsh/cornish...entierly ‘P’ celts?.
The settlers in Britanny were displaced refugees from the southwern part of our island, escaping from the saxons (saeson) who went on to occupy all of what is now known as england.
The english are mainly a germanic people and have only really been on the island for 1,500 years , which is relatively recent. There are trees older than that.
How that translates to the present day is probably inconsequential. I know that genetically the cornish are really celtic, they have very little gentic influence from the english. Culturally though , I imagine the state of their language would give the best insight into their cultural identity. Predominantly I’d say they consider themselves english.
I remember arriving in Plymouth ferry terminal the day england beat us in the euros and I think I’d have been asking for trouble or at least hassle walking around in my wales top. Not much sympathy would have been received.