I got it done pretty late, maybe 17/18 so i'm sure you could get it on the NHS at 20.
Make a GP appointment, they will refer you to a surgeon on the NHS and it goes from there. Such a minor operation, its usually a day-surgery.
Not as bad as the person's comment above either, a little uncomfortable, you have to wear a bandage around them for a week, and after that comes off you just need to sleep with a head band round them. Heals pretty quickly and not much pain involved.
Good luck