The 3 most important purchases:
CPU: Intel Core i5-3350P: £127.49
3.1ghz processor, 4 cores (actually has 4, rather than the i3 which has 2 cores with 2 "threads" per core). Currently top of Tom's Hardware's mid-range gaming CPU suggestions and this will last you for years. Doesn't matter that it's based on Intel's 3rd generation (the 3000 naming) rather than the brand new 4th generation and the improvements are minimal for the price increase.
Graphics Card: Geforce GTI 650 Ti BOOST 2gb: £124.38
Great graphics card. Also from Tom's Hardware's list. However, they have the 1GB listed for around £120 price mark and Scan are doing the 2gb model at the same price. Which is great. Card is completely "future proof" unless you try and run it through a 4K television, but then most graphics cards choke on that anyway including the high-end ones. If you're looking around for other shops ensure you get the "BOOST" version of this card. The regular version is much lower in spec (the BOOST is a bit of a hybrid between the 650 and 660).
This card is currently out of stock with Scan (not surprised) but they usually honour pre-order prices if it goes up. If they're unable to then you'll get an email asking you if you want to cancel the order (and get a refund).
Power Supply: Corsair 500w CS Builder: £46.84
500w is more than enough to power this CPU/GPU combo. Corsair are an excellent brand (NEVER BUY CHEAP GENERIC PSUs!!!) and I've personally used the builder ones in a number of machines and they've worked perfectly. The one linked above has a good enough 12v rail (don't ask, just accept) to power the graphics card listed too.
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That all comes to £298.71. To finish it off you need a motherboard, RAM, case, hard drive, DVD drive and your mouse and keyboard. For these you can go for the "cheap and branded" route on all of them.
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Motherboard £47.00: http://www.ebuyer.com/363618-msi-b75ma-p45-socket-1155-vga-dvi-8-channel-audio-atx-motherboard-b75ma-p45
Does what you need. Cheapest full-sized motherboard (microATX motherboards have issues with cases and ventilation). Has USB3.0 support which is nice (and rare at that price). Cheapset is cheap, but cheap means doesn't have all the bells and whistles to support overlocking rather than being shit. One bad comment about it not recognising XP3 or a SATA hard drive - I have no idea what that guy is on about as the mobo does that fine (and XP3 has known issues with SATA drives). Even if this was somehow a legitimate issue, you're using Windows 7 which has none of these problems.
8gb RAM: £57.58: 2x http://www.ebuyer.com/394560-kingston-4gb-ddr3-1333mhz-memory-kvr13n9s8-4
RAM has 2 stats that actually impact performance: transfer speed and timing. For transfer speed, 1333mhz is fine and you won't notice the difference for the higher stuff unless you do nothing but run benchmarks (for gaming, your CPU or GPU will be choking long before RAM becomes an issue, as games do not need massive RAM through-put). The timings is completely useless and you will never notice the difference between CL6, CL9 or CL10 ram.
For some reason getting two single sticks of 4gb was much cheaper than the 8gb kits containing 2x4gb sticks. Don't be put off by the "value" part of the RAM - it's made by Kingston so will still be top quality and won't break. The value part means it's utterly rubbish for overclocking (which you won't be doing anyway) and other fancy hardware tweaking.
Don't buy a single stick of RAM either - always do it in pairs (i.e. get 2x4gb rather than 1x8gb) as it means you get the full speed from "Dual Channel" motherboards (which the one I linked is). Pretty sure 1 stick = half the speed, which you will notice.
Case: £34.98 http://www.ebuyer.com/233740-coolermaster-elite-430-all-black-interior-mid-tower-case-with-side-window-rc-430-kwn1
Bargin. You will get usable cheaper cases, but the airflow will be crap, the construction will be crap and they probably won't have USB3.0 on the front. Great case, great manufacturer, USB3.0 on the front along with the usual other ports, isn't as tall as most full-sized cases (this is a good thing as most of that space is just wasted), supports stupidly long graphics cards (not sure if the one linked is) and will basically last you for life.
A couple of the comments on the ebuyer page are slating it. I got worried, looked up some reviews and it's actually gotten a lot of praise from good tech-review sites. It is still an entry level case, but for what it offers at £35 it can't be beaten. In addition, it also has screwless fittings for some of the accessories (hard drive, DVD drive) which will make them much easier to install.
500gb HD: £37.98: http://www.ebuyer.com/272944-seagate-500gb-barracuda-internal-hard-drive-st500dm002
1tb HD: £44.98: http://www.ebuyer.com/319639-seagate-1tb-barracuda-internal-hard-drive-oem-st1000dm003
Pick one. 500gb is fine. 1tb means you can be REALLY lazy when it comes to not uninstalling things and amass a gargantuan collection of porn and illegal movie/music downloads.
DVD writer: £11.98 http://www.ebuyer.com/506016-samsung-24x-sata-internal-dvd-rw-bare-black-sh-224db-bebe
Because it's only £2 more expensive than just getting a reader. OEM means no cables. I have 100% no clue if the motherboard comes with any (you'll need one for the hard drive and the DVD drive), so treat yourself to...
2x SATA3 cables: £1.68: http://www.ebuyer.com/248882-xenta-sata-3-cable-6gbps-46cm-est-sata3-0
Just in case
Grand total of: £496.91 (with 1tb drive). Which of course, leaves you no money left for the wireless keyboard and mouse. lol. You can easily get away with dropping the graphics card down to something cheaper. However, before you do I suggest you shop around for cheaper versions of the stuff I posted. You should be able to get some bits cheaper from Amazon, just make sure it's free delivery (if shipped via Amazon then you can get it with Super Saver, otherwise if it's a 3rd party you'll need to check on the product page).
Big issue with all of this is that it needs assembling yourself which is actually very easy nowadays as all of the connectors only go one-way and pretty much everything just plugs in and works. You will never get as good a PC for whatever you're willing to spend if it's prebuild than had you built it yourself as the builders will use lower-performance parts and include their labour time in the price. The profit margins on PC components are thin before factoring in staff wages for building the thing. Once you've built one, all future PCs (or even just upgrades) are the simplest thing in the world.