£3.3k is about right, this is what I paid. You also have to pay about £50 per half hour physio session plus follow up appointments at approx £75. Although I went privately, I then phased back into the NHS for a further op that was needed. If you are on the NHS waiting list, you can op to be put on for a cancellation. You would not get a lot of notice for a cancellation, but sometimes it is worth it. I was given 9 days notice to have my op, as this was a cancellation however when going privately you can chose when you go in. If you have it done in UK at least you get your physio as well.
I would second what Vickster said, I would not have wanted to go abroad for surgery, we have brilliant surgeons over here.
You have my sympathy if you have a torn meniscus. Been there, done that one. Please bear in mind that even after having the arthroscopy, it may not solve all your issues. I had one in March 2011 and then needed another op, which I had in November 2011. Could you get a knee brace to help. Make sure you keep on top of the pain with pain relief, and ice it your knee as well.
Good luck and let us know what you are going to do.