Being from the UK myself, I could suggest quite a bit. How long are you staying? Definitely check out the London Eye, which is the big ferris wheel that gives you a really nice overview of London and surrounding areas. It's also next to the Aquarium. You can check out St. James Park, which at the end sits Buckingham Palace. At the other end of St. James Park is Trafalgar Square and the British National Museum. At 1100 hours every morning, you can witness the changing of the guards. In the Jewel House, located in the Tower of London, you will find the famous Crown Jewels. For shopping, there is Piccadilly Circus, which has all of the upscale stores we are used to here, and more. If you're feeling adventurous, rent a car and drive out about an hour west to Stonehenge, or you can head southeast about 1.5 hours to Dover, to see the famous white cliffs. There is a lot to do.
With regards to gaybourhoods, most popular is Old Compton Street in the SoHo District, which is kind of London's gay mecca.
Definitely enjoy your trip!