Heya, I didn't have surgery for an overbite but I did have it for an underbite, which is a pretty similar-ish procedure (braces, operation, recovery, liquid diet etc!)
It was a pretty long timeline - I had braces from when I was 13, then I had the surgey when I was 16, just after I started college. I don't know if you've already had braces or if you'd still need them or anything, so that might be different for you? It is a good idea to think about when you'll be having it done, because it depends how long you'll need off afterwards - I was originally going to have two weeks off college, but I ended up missing four weeks off college (and then having two weeks off for Christmas, so really I had 6 weeks off). I don't think I could have gone back before that though because it's really exhausting when you can't open your mouth enough to speak (or breathe through your mouth at first!). Although I was very, very anaemic at the time, so I don't know if that made a difference.
But although that makes it sound really negative, it was
definitely worthwhile having the operation - it made so much difference to my jaw appearance, I'm so much less self-conscious about that now.
The recovery isn't nice, but it really really is worth it. There was a lot of swelling for the first couple of weeks, but obviously it goes down so if you do decide to have it don't worry too much about that! The liquid diet is really frustrating (especially when your friends and family sit and eat in front of you >.<), I had my jaw surgery in mid-November and started eating proper meals again the week of Christmas, so about 4 weeks I guess. You kinda live off soup and build-up milkshakes for a while (and even soups were too thick for me at first >.<), but I definitely wouldn't change it because it was worth it.
I'd assume it must be possible even with the budget cuts with the NHS, so I wouldn't worry about that though.
Erm, I can't really think of anything else but if there's anything you want to know about the recovery/liquid diet/surgery part I can tell you as much as I can! I know it's a slightly different op, but it's similar recoveries/preparation etc.