Uk may not even offer the surgery... The NHS are very reluctant to put you forward for surgery if at all avoidable. I was in a very similar situation but lived in the USA, i had seen doctors there and they said i needed surgery for a rotator cuff injury on my shoulder as it kept dislocating, Also i have worn down the tissue on my socket which makes it slide in and out easy. Anyway i couldnt do this in the USA as cost a fortune.. Over $100,000 and i had no insurance to cover it.. So i flew back to the UK after 12yrs in USA made an appointment at my Drs who referred me to a specialist... WOULD NOT GIVE ME SURGERY!! This went on for months.. and second opinions chats with physios all told me NHS really dont want people being put in for surgeries unless absolutley necarssary as it cost so much.........All im saying is check that this surgery is definitely needed because what the NHS class as needed is different from what the docs may have told you here.
Edit to say... 4 yrs on i never did have the operation , I did 6 months physio then gave up i just ate painkillers and ibruprofen, gave up my job in the States as i needed a good shoulder for my job.