This is obviously a bit over, but I reckon there is quite a jump in performance between this price and say £50 lower.
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
CPU: Intel Core i5-3470 3.2GHz Quad-Core Processor (£146.34 @ Aria PC)
Motherboard: ASRock H77M-ITX Mini ITX LGA1155 Motherboard (£79.19 @ Amazon UK)
Memory: Patriot Intel Extreme Master, Limited Ed 8GB (2 x 4GB) DDR3-1600 Memory (£36.23 @ Amazon UK)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive (£50.00 @ Ebuyer)
Video Card: Club 3D Radeon HD 7870 XT 2GB Video Card (£171.62 @ Amazon UK)
Case: BitFenix Prodigy (Orange) Mini ITX Tower Case (£62.27 @ Amazon UK)
Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply (£48.17 @ Aria PC)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer (£11.79 @ Amazon UK)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) (£68.04 @ CCL Computers)
Total: £673.65
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-03-20 22:38 GMT+0000)
Went with the orange Prodigy because I think it looks awesome, but I have a black one myself.
For gaming on an ITX system you don't have a huge amount of options when it comes to CPUs. AMD only really make APUs for ITX, and using one of those with the intention of having a bespoke card doesn't make a huge amount of sense. Conversely, you can use any current gen Intel CPU, but with the way games are progressing you probably are going to want a quad core, and for that you need an i5. Cheapest i5 will effectively be the 3350P, but I stuck in a 3470 as it is a bit faster clock speed and also has better out of the box turbo mode. The difference is £7.
Graphics wise, you specified a HD7870, but personally I don't see why anyone in the UK would buy one right now. HD7870s start at around £165 but for £172 you can have a HD7870XT which is really just a lightly crippled HD7950. The GTX660 is a solid option because of it's compact size and better power use, but right now it's too expensive relative to the HD7870 and not as good overall.
If you need/want wireless, swap the motherboard for the Gigabyte GA-H77N-WIFI, it's around the same price.