Most Scots and Cymry do not identify as British, and do not like it when you refer to them as British.

I'm Scots, not British. Roughly 50% of us support independence from the UK.

A majority of people in North West England has Irish ancestry. Are those people not British?

That’s my point. There’s not really a singular “Brit” unless you designate one group to decide, and various other groups may also want to be considered British or not. Since I’m from the US, I won’t say more, because I’m sure there’s more to this I’m missing.