We don't all have the same experience of life, so I preface this by saying that this is just my experience.

UK life can be somewhat tribal, like anywhere, but I don't recognise your framing of the UK as "deeply classist" nor do I think any classism is as one way as you paint. I grew up lower middle class/working class in very working class areas (council estates, ex-mining villages/towns, that sort of thing). Two of the worst things you could be in those areas was "posh" or from outside the area. So called inverse snobbery was a big thing. If anything, though, not being local was a bigger cause for feeling like an outsider.