As Shanks says a term commonly used in the UK is Asian meaning "from the Indian subcontinent".

I suspect that this is because our largest non-white ethnic grouping (less than 4% of the whole UK is non-white, maybe slightly higher now) is from the Indian subcontinent and most people from Pakistan would prefer it not to be assumed that they are from India, so we don't try to guess and stick with Asian as a "safe" bet. South Asian is sometimes used by intitutions but isn't an every day term used in the street.

Apart from London, which seems to include people from every nation on earth, we don't have the same level of large scale immigration from South East Asia as the USA or Australia.

There are Chinese people in small numbers all over the country and a few large clusters in some big cities. I think we tend to use the name of the country for people from China, Korea, Japan or anywhere else in Asia (North or South)

"African and Carribean" used to be the other term but I'm not up to date on how people now choose to describe themselves.

The term we don't seem to use very often is "Caucasian" - it always stands out in American cop shows.

Here's the data from the CIA Worldfactbook 2000:
Ethnic groups: English 81.5%, Scottish 9.6%, Irish 2.4%, Welsh 1.9%, Ulster 1.8%, West Indian, Indian, Pakistani, and other 2.8%