Answer by Clyde Davies:
We'd do it gradually and insidiously. First, we'd start exporting TV series like Sherlock to you and getting you to like them. (We'd subsequently start exporting the actors that appeared in those series.)
Then, you'd start using British aphorisms and expletives like 'bloody' and 'wanker', possibly together. Finally, you'd end up playing our national sport and being better than us at it.
But that could never happen in a month of Sundays! Could it?
Addendum: we're still working on getting you to realize that 'beer' is not a word for a wan liquid that looks and tastes like gnat urine. Until that day comes, we might well invade but we wouldn't stick around for very long.