In my experience, most Europeans speak English with an accent which comes from their own language. I know some who have lived in Britain for decades and are fully fluent, but who speak with a French or German or Italian accent. The most difficult professional relationship I have had, in terms of intelligibility, was with the manager of a Japanese business in Scotland whose accent was a mixture of Japanese and Glaswegian. I usually had to ask him to put the matter in writing.

For the relatively few for whom this is not the case, I would say they usually speak with an American rather than British accent. The influence of American films, music and TV is too strong. For that matter, American usage is increasingly common among young British speakers. One that particularly irritates me is the use of "alternate" instead of "alternative" which loses a useful nuance.