All right, I've got a list of parts from Scan.
First, the ASUS M5A97 [http://www.scan.co.uk/products/asus-m5a97-amd-970-s-am3plus-ddr3-sata-iii-6gb-s-raid-sata-pcie-20-%28x16%29-atx]. This motherboard uses AM3+, so you'll be future-proof for quite a while when it comes to upgrading your mobo. It also has a few USB 3.0 ports, because why not?
Second, the AMD Phenom II X4 965 [http://www.scan.co.uk/products/amd-phenom-ii-x4-965-black-edition-s-am3-34ghz-8mb-cache-125w-retail] CPU. It's still one of the highest-clocked quad-core CPUs that AMD offers, and gaming doesn't currently benefit from hex- or octa-core CPUs, so this is probably the best price/performance ratio you're going to get.
Next, 8GB of Corsair Vengeance [http://www.scan.co.uk/products/8gb-%282x4gb%29-corsair-ddr3-vengeance-jet-black-pc3-12800-%281600%29-non-ecc-cas-9-9-9-24-xmp-150v] RAM, clocked at 1600 MHz. This pretty much speaks for itself. The mobo supports 32GB if you ever need to upgrade, by the way.
Next, a 1TB Seagate Barracuda [http://www.scan.co.uk/products/1tb-seagate-st31000340ns-barracuda-es2-enterprise-24x7-sata-3gb-s-7200rpm-32mb-cache-95ms] HDD. 1TB will suffice for all your gaming needs, plus most (probably all) multimedia you have on your computer.
Next, the Sapphire Radeon 6770 [http://www.scan.co.uk/products/1gb-sapphire-hd-6770-4000mhz-sdram-gpu-775mhz-800-cores-eyefinity-d-sub-dual-link-dvi-i-hdmi]. I haven't personally experimented with the 6000 series, but from what I understand, they are roughly equal to the 5000 series. I myself have a 5770, which handles every game I throw at it, Crysis, Skyrim and Battlefield included, with no problem.
Next, a Cooler Master 800W [http://www.scan.co.uk/products/800w-psu-coolermaster-silent-pro-gold-80ga-d3-modular-90-eff-80-plus-gold-sli-crossfire-eps-12v-quie] PSU. It's 80 Plus Gold certified, and has enough overhead to account for any major upgrades you wish to make.
Next, a Sony DVDRW burner [http://www.scan.co.uk/products/sony-ad-7280s-0b-24x-dvdr-12xdvddl-dvdplusrw-x8-rwx6-12xram-sata-black-oem]. If I have to fucking explain this one, there's no hope for you, OP.
Finally, a case which is a personal favorite of mine, the Cooler Master HAF 932 [http://www.novatech.co.uk/products/components/cases/cases/rc-932-kkn5-gp.html], which I had to head to Novatech for. It's not too fancy, but it's a beast at keeping your system cool, and it does so fairly quietly, in my opinion.
Total cost comes out just below £700. Use the extra to, I dunno, buy yourself a joystick or something hahaha. Hope this helps, OP.