You're right that generally "Asian" would be used more for countries like India/Pakistan than China/Japan/etc. but, at least in the south of England, there's no dearth. Oriental restaurants and takeaways that I've seen have nearly all been run by east Asians (I couldn't 100% say I always know from which country, but imagine largely inline with the cuisine they're serving) - in Oxford, London, Cambridge, Peterborough, Northampton.. and that's been my same experience pretty much anywhere else I've been in the UK. But could well be different up north for example.