Our movies are viewed as American pandering jokes in Europe and as inconsequential by the Americans... So I have heard.
So I suppose the UK has little or no influence on global film.
We occasionally throw up a director like David Lean or Alfred Hitchcock who gain followings in the movie community oversees... and the James Bond franchise greatly influenced Spielberg's 'Indianna Jones' movies... and 'The Battle of Britain' had some influence over the Death Star battle in 'Star Wars' but those are only little things.