Check Ebuyer... you'll probably need to buy a cheap starting unit, then add an entry-level graphics card yourself. Good graphics cards will typically require upgrading the factory power supply on pre-built units in your price range.
http://www.ebuyer.com
CyberpowerPC and PC Specialists make good gaming computers, but they're more expensive than what I've suggested.
Here is a decent pre-built unit:
http://www.ebuyer.com/409310-cyberpower-gaming-battalion-502-pc-ecc01142
Here's an even better deal on Amazon. I'm unfamiliar with the seller and the price only includes hardware, so you'd have to spend another £70 for a copy of Windows and install it yourself (unless the seller offers that for an additional fee)
http://www.amazon.co.uk/ANKERMANN-PC-WildCAT-Cardreader-24xDVD-Writer-warranty/dp/B009P0XV52/ref=sr_1_6?ie=UTF8&qid=1362621769&sr=8-6
Both will play demanding games on high (but not ultra) settings smoothly. Skyrim, Battlefield 3, Arma II etc... Easier games like WoW will play fine on ultra.
The 2nd computer has a better graphics card, so you'd get higher fps with that one if you're willing to deal with the Amazon marketplace seller.
http://www.techpowerup.com/reviews/Zotac/GeForce_GTX_650_Ti_Amp_Edition/8.html