You may find better luck going to a specific game studio. There are many in and around London, with Media Molecule in Guildford and London Studio in, well, London. I know Rockstar are up north in Scotland. What type of game is it? Genre? Story? Special features (multiplayer, etc) What presentation style are you after? Linear, like Uncharted or God of War? Open world? Saints Row, Grand Theft Auto? Do you have blueprints, demo videos of how you envisage the game to look?
Ultimately it's extremely difficult, near impossible to get replies from half of these studios, and the other half that do reply are likely to shoot your pitch offer down without even hearing any details about your game. Not trying to push your spirit down mate, it's just the truth.
The best way to get a good chance to pitching your game idea to a studio is to have a contact. If you don't have a contact it's best to start making them. Try attending gaming conferences and expos, Eurogamer, Gamescom, and any electronics conferences that Sony may be attending.
Good luck mate)
(If your idea turns into a full blown video game, I want a free copy!)
