If the dentist says they need to come out, he may send you to hospital to have them done under a general anaesthetic (if he suggests this say YES!!).
I had all mine out a few years ago, at the hospital, and it didn't cost a penny as it was paid for by the NHS. I don't think it matters if the dentist is not NHS - the op itself is as a result of a referral and therefore shouldn't cost you. Hurrah for the NHS - a great British institution.
The procedure is quick and, as you'll be asleep, painless too. There were 4 of us on the ward having wisdom teeth out. None of us had any complications. It's obviously a bit sore where the teeth were, and your cheeks/jaw can be a bit swollen, but other than that no problems. On the pain scale (and having given birth), it's a mere 2.
Good luck natalie_1982!