I think it depends on the websites and you probably would have to give a try. Some of them require a US credit card, some other don't.
I have the same problem with the US NWA.com. I use the Asian NWA website (with a european credit card) which have similar prices than the US and it works fine.

If you can't book on the airlines website, you might want to check with travel websites like travelocity/ orbitz/ expedia, they usually have similar prices than airlines websites (but charge a booking fee). I know for a fact that Travelocity accepts non US credit card - I've done it a few months ago.

If this does not work either, try to book via a US based travel agent. Now that most of the tickets are electronically issued, there shouldn't be too much of trouble to get it "delivered" to you in the UK