The company I know about is Airkix, here's a bit from their blurb:
At the moment, Buyagift are offering a package for two people down to £49 from £98. Plus you get 11% cashback from imutualAbout Indoor Sky Diving
The unforgettable sensation of flying awaits you at Airkix, a sensation that few people ever get to experience. But at Airkix we believe everyone should have the opportunity to experience flying. With three centres offering indoor skydiving, in Basingstoke (opening Summer 2013), Manchester and Milton Keynes, wherever you are in the UK you're never too far away from the sheer joy of human flight. Safe and fun, our highly qualified and experienced indoor skydiving instructors will teach you how to fly, step by step. Once you've discovered the thrill of an indoor skydive with Airkix, you'll understand why so many people come back time and time again. If you're looking for the best indoor sky diving in the UK, look no further than Airkix.
Body Flying
Indoor skydiving is also known as body flight or body flying and Airkix Milton Keynes was the first of its kind in Europe, with Airkix Manchester the second and Airkix Basingstoke the third. It's no wonder then, that Airkix offers the most exciting and advanced body flying experience available in the UK today, one that people from across the country have come to try and love. Once you’ve sampled body flying in Basingstoke (opening Summer 2013), Manchester or Milton Keynes with Airkix, you’ll soon realise why we're known as the Smile Factory, giving everyone aged 4-104 the opportunity to experience the thrill of flying. You'll soon learn how to gain total control of your flying, grasping the bodyflying basics of moving up, down, forwards, backwards, sideways and turning. When you consider that the introductory Kix-start experience provides you with three times the freefall of a tandem skydive at a fraction the price, you'll see why so many come back to experience the thrill of bodyflight again and again as they become one of our Pro-flyers.