We don't say "the toothache" but we do say eg. "the measles". So I think it's more an older way of talking than a Britishism. As for "on accident" I've always

We don't say "the toothache" but we do say eg. "the measles". So I think it's more an older way of talking than a Britishism. As for "on accident" I've always assumed this was just a mistake from childhood, kids equating it with "on purpose" and never being corrected. A bit of a bone apple tea. However I get your point, I used to correct an Indian colleague when he would say expressions a bit wrong, until I gave up and realized it had just become part of his local dialect in the region he was from. (Eg. "I have to go pick my kid" instead of "pick up my kid" which made me laugh at first and then drove me a bit crazy because he would consistently keep saying it.) At some point these things cross a line and become somehow "correct" again, that's just language for you. A native English speakers we are in a particular spot where we have to just accept that the majority of the world is going to be speaking our language non natively, and that is fine once you get used to it.