I didn't know if you had a Nvidia or AMD preference for graphics cards, so I set up two fairly similarly performing configurations, one AMD and one Nvidia.
AMD:
http://pcpartpicker.com/uk/p/nd6s
Total: £1159.07
Nvidia:
http://pcpartpicker.com/uk/p/nd6Y
Total: £1144.98
The AMD is somewhat faster, but the Nvidia uses somewhat less power and is slightly cheaper.
If you want me to really fill up your budget with two monster machines, just say so and I'll revise them, but these should be great machines. I included a new 1080p LED IPS display with a low response time as well as Windows 7 Home Premium x64.
The CPU in both systems is about as good as a gaming CPU can get right now (spending more won't increase gaming performance). I got a decent cooler for some overclocking and expect about 4.3GHz to 4.5GHz to be where you can get to in overclocking it.
Faster memory than dual-channel DDR3-1600 9-9-9-24 really doesn't make much of a difference at all in gamign performance on this platform and more than 8GB makes even less of a difference, so I threw in the cheapest kit that fit the job. Paying more will not improve performance noticeably here.
Vertex 4 is easily the second fastest SSD on average (Samsung 840 Pro, much more expensive, takes the lead) despite being among the cheaper models and this Caviar Blue is among the fastest consumer hard drives as well as a reliable model with an excellent price.
ASRock Extreme 4 is one of the most underrated motherboards of them all. It's a high-end board with a lower mid-ranged price and that makes it generally the number one recommendation for an LGA 1155 build from me and most other Tom's forum goers.
Both of my video card choices are the best from either camp or effectively equal to the best despite being among the fairly cheap models. What can I say, I look for bargains and Zotac and Gigabyte really came through this generation in that right now.
This case is excellent for the price. It's a sub 30 pound case with an excellent cooling setup and a few more fans can be added if wanted, but I doubt that it'll be necessary.
I chose one power supply per build to suit the graphics card. I gave the AMD build a higher wattage, more efficient unit, but both are great quality and modular.
Last is the optical disk drive... Well, it's the cheapest that I could find. I see no reason to splurge on such a drive unless you want Blu-Ray playback.