PCPartPicker part list:
http://uk.pcpartpicker.com/p/17pb5
Price breakdown by merchant: http://uk.pcpartpicker.com/p/17pb5/by_merchant/
Benchmarks: http://uk.pcpartpicker.com/p/17pb5/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor (£87.76 @ Aria PC)
Motherboard: Gigabyte GA-970A-UD3 ATX AM3+ Motherboard (£77.88 @ Dabs)
Memory: Kingston Beast 8GB (2 x 4GB) DDR3-1600 Memory (£49.99 @ Dabs)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive (£44.99 @ Aria PC)
Video Card: PowerColor Radeon HD 7870 XT 2GB Video Card (£180.42 @ Ebuyer)
Power Supply: XFX ProSeries 450W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply (£36.18 @ Aria PC)
Total: £477.22
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-06-17 19:13 BST+0100)
Ok there's a set of components which should game pretty well. The motherboard I've chosen is good for overclocking as well, so you could get an aftermarket cooler for christmas and overclock. Notice it's at the £480 mark; this leaves you room to get an OS. However, it also assumes you can get a case, monitor, keyboad and mouse and stuff for free, and the PSU is a little weak. If you had to fit a case and dvd drive as well, it might turn into this:
PCPartPicker part list:
http://uk.pcpartpicker.com/p/17pkE
Price breakdown by merchant: http://uk.pcpartpicker.com/p/17pkE/by_merchant/
Benchmarks: http://uk.pcpartpicker.com/p/17pkE/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor (£87.76 @ Aria PC)
Motherboard: Gigabyte GA-970A-DS3 ATX AM3+ Motherboard (£52.82 @ Aria PC)
Memory: Kingston Beast 8GB (2 x 4GB) DDR3-1600 Memory (£49.99 @ Dabs)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive (£44.99 @ Aria PC)
Video Card: XFX Radeon HD 7850 2GB Video Card (£141.62 @ CCL Computers)
Case: Xigmatek ASGARD PRO (Black) ATX Mid Tower Case (£34.17 @ Dabs)
Power Supply: XFX ProSeries 450W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply (£36.18 @ Aria PC)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer (£12.99 @ Dabs)
Monitor: Hannspree HE225DPB 21.5" Monitor (£88.51 @ Amazon UK)
Keyboard: Gigabyte GK-K6800 Wired Standard Keyboard (£8.50 @ Ebuyer)
Mouse: Gigabyte GM-M5050 Wired Optical Mouse (£1.41 @ Amazon UK)
Total: £558.94
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-06-17 19:22 BST+0100)
That one has a weaker GPU, and a motherboard that you can't really overclock on; it does, however, have a monitor.
One final point - none of these builds have an OS with them. If you need windows, it sets you back an extra £70, so it may be worth going linux or using a trial edition of windows to save up money for the full version.