They're "doing business" there by serving ads to their citizens, that's the legal basis for suing them. Whether that goes anywhere depends on the laws governing the business and any leverage UK has (say, going after advertising who do business with the company and in the UK).

I think it only works if the country you are in allows it to happen, as in they have an understanding with the UK (in this case) to follow through with legal stuff. If they were in russia (for example), the UK probably couldn't enforce anything.

Think it is down to the government of your country.