To fly a US reg bizjet you need either an FAA licence or a licence from the state whose airspace you are in. If you are not in UK airspace then a CAA licence is so much scrap paper. Even a JAR licence is a bit of a grey area. The FAA are happy with it, but I'm not sure I'd like to try and explain to a French inspector that I was flying a US registered aircraft on a UK issued licence in France...