I was done about a year ago. We looked into both and while I would have preferred private due partly due to a supposedly slightly better procedure (tiny incision / cauterisation as opposed to cut and tied) but mainly due to being able to get it done quickly and at a time to suit, ultimately £495 is £495. So I went to the GP, got quizzed about how serious I was, etc., and then she agreed to add me to the list. At which point she said that the local NHS Trust had decided to outsource the job to the same clinic I'd looked at spending £495 on! Only difference was a 3 month wait after which i got a letter asking me to ring and make an appt as if I was a paying punter.
Procedure was fine, a bit uncomfortable, but once you've lain naked from the waist down on a table while a nurse pulls your nuts through a hole in a sheet and paints them with antiseptic, you'd give anything to be out of there asap and without catching anyone's eye again.
To cover it all; post op took me about 4 weeks before I could cycle again but that was due to a minor wound infection which stopped the healing process, meaning I needed the wound cleaned right out and start the healing again after about 2 weeks. The actual nut discomfort was no big thing, fixed with Nurofen.
And paddling in the sea without your wellies on is so much better.