I also think you would lose if you tried to sue, particularly if the .co.uk, for example, was bought by a UK citizen.
A certain online bingo site (not one accredited by CAP, I hasten to add) with a very generic name threatened to sue me for using the same two words in a domain I had that promoted BingoHall.com.
They accused me of passing off, trademark infringement and all sorts of things. I got registered letters from their lawyers in Canada and all that. So I called them, told them that they had no case, pointed out their trademark didn’t cover the UK and asked them very politely to desist from threatening me otherwise I would be the one sueing.
That was the last I ever heard from them.