That would be such a mistake and only serve to cause more division, because as you say, the UK would never accept it. Neither would multiple countries already in the EU that also use their own currency.

The EU, generally, are pragmatic. They'd much rather get other concessions than wasting political capital on trying to enforce the Euro on the UK.

E: downvote all you like, but that's realpolitik. The EU isn't going to pass up the second largest economy in the continent over something so trivial that they don't even pressure much smaller countries into it. Pure fantasy from people who don't have a clue.