New Gaming Build Sub £400

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-3470 3.2GHz Quad-Core Processor (£143.40 @ Aria PC)
Motherboard: MSI B75MA-P45 Micro ATX LGA1155 Motherboard (£41.40 @ Aria PC)
Memory: Patriot Intel Extreme Master, Limited Ed 8GB (2 x 4GB) DDR3-1600 Memory (£36.23 @ Amazon UK)
Storage: Hitachi Ultrastar 1TB 3.5" 7200RPM Internal Hard Drive (£46.86 @ Aria PC)
Video Card: XFX Radeon HD 7850 1GB Video Card (£125.68 @ Aria PC)
Case: Xigmatek ASGARD PRO (Black) ATX Mid Tower Case (£34.96 @ Dabs)
Power Supply: XFX ProSeries 450W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply (£34.99 @ Aria PC)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer (£11.45 @ Amazon UK)
Keyboard: Logitech MK120 Wired Slim Keyboard w/Optical Mouse (£18.40 @ Amazon UK)
Total: £493.37
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-03-11 17:47 GMT+0000)

better parts, and not from ebay's potentially fly-by-night sellers

Better, but also considerably more expensive.
I'll think about it, but I haven't really got that much money to play with.

ok, I can trim that by £100:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-6300 3.5GHz 6-Core Processor (£101.94 @ Aria PC)
Motherboard: MSI 970A-G46 ATX AM3+ Motherboard (£47.94 @ Aria PC)
Memory: Patriot Intel Extreme Master, Limited Ed 8GB (2 x 4GB) DDR3-1600 Memory (£36.23 @ Amazon UK)
Storage: Seagate Barracuda 500GB 3.5" 7200RPM Internal Hard Drive (£39.56 @ CCL Computers)
Video Card: MSI Radeon HD 7770 GHz Edition 1GB Video Card (£84.54 @ Aria PC)
Case: Cooler Master RC-361-KKN1 (Black) ATX Mid Tower Case (£26.34 @ Aria PC)
Power Supply: XFX ProSeries 450W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply (£34.99 @ Aria PC)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer (£11.45 @ Amazon UK)
Keyboard: Gigabyte GK-KM6150 Wired Standard Keyboard w/Optical Mouse (£9.95 @ Aria PC)
Total: £392.94
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-03-11 18:22 GMT+0000)

I think that's a pretty well balanced PC. THe HD 7770 is a good performing graphics card for the price. And it's the new generation of AMD cards. I'm not too familiar with the CPU you chose. But I know it's 3 years old. For a newer option try the FX 6300 or FX4300. They're a little more expensive at 129.99 and 119.99. But I bet they perform better too and it's a new model CPU AND it can overclock really high if your interested in that. If you want to overclock you might need a little bit better MoBo and a CPU Cooler. For the CPU cooler the Hyper 212 Evo is only 20 bucks and performs well. So for about 75 extra bucks you can have a way better PC in my opinion.