NHS usually equals difficulty persuadig them to do the op, as its for cosmetic gain as opposed to health benefits.
USA surgery works out slightly cheaper due to our exchange rate, although not by much. For example a top notch surgeon in the states charges 6-7k, and here about 4k. Factor in travel and hotel stay for 7-10 days and it becomes more expensive.
Your cheapest option is surgery in Europe. The poland thread (many pages) in this section is all about the cheaper option. Think South Africa is another place offering cheap surgery.
Good luck.