I think the British government should ask Paramount for a formal apology over this, as well as a promise that the mistake will be corrected whatever the cost. If they don't, then Parliament should ban the movie in the UK. I smell diplomatic incident!
By the 22nd century the Monarchy was dissolved and Parliment redesigned the flag in a different albiet similar pattern.
Since Star Trek is fiction
... lets rewrite British future history to fit Star Trek on screen.