If you go for an AMD chip (rather than intel) a 4core at 3.2ghz should run the games well and save you about £100 over the Intel. Scour site such as ebuyer.com and dabs.com. For my rig I picked up an ATI 5850 ddr5 1gb for £180 (sapphire) when the similar spec cards were all in the £250 price bracket.
If budget is an issue I really would look at building it yourself rather than buying from PCWorld or the like - that will save you another 10-20% easily and it really is quite simple to do as most components slot in (and this forum is great for help too!)
I had a quick look and for similar money mentioned (300-400 + monitor/windows software) you can get the following:
{Disclaimer - This was literally a 5 minutes check for components - before you buy everything make sure that a) all products are compatible - e.g. the mother board is for the Intel/AMD chip you buy and can connect to the other components - the RAM is the right type - the PSU has enough power to run the machine - all products can fit inside the dimensions of the tower}
PSU:
http://www.ebuyer.com/124927-arctic-power-700w-psu-4x-sata-1x-pci-express-p2-arctic-700td
£43.98
(You may not need 700w - but any lower than 500w would be pushing the limits. Bear in mind this option means you can upgrade components as you need to, so for an extra £10 today, saves you another £50 later down the line. You may also save cash by buying the PSU and case together)
CPU:
http://www.ebuyer.com/190673-amd-phenom-ii-x4-955-black-edition-socket-am3-3-2-ghz-6mb-hdz955fbgmbox
£91.52
(Black Edition means you can easily 'overclock' it (speed it up!) if you want a bit more performance later in life - but don't worry about it for now!)
I think this one would do the job:
http://www.dabs.com/products/amd-phenom-ii-x2-555-3-2ghz-black-edition-socket-am3-6mb-80w-6NCH.html?refs=4294946173 at £66.50 (3.2ghz dual core) but this is pretty much the lowest spec for today's games, so in 6 months time you would find games only worked on their lowest resolutions, were a bit sluggish.
RAM:
http://www.ebuyer.com/173122-corsair-4gb-2x2gb-ddr3-1600mhz-pc3-12800-xms3-i5-memory-kit-cl9-9-9-9-24-1-65v-cmx4gx3m2a1600c9
£24.58
(A steal at £24.58)
Monitor:
http://www.dabs.com/products/philips-v-line-18-5--led-monitor---dvi-vga-5ms-built-in-speakers-7NQ3.html
£80.00
Nice size, HD, built-in speakers
Motherboard:
http://www.dabs.com/products/asus-am3--amd-760g---sb710-ddr3-atx-7JG3.html
£38.46
(Great budget board, works with the Phenom II chip - just make sure the RAM is also supported)
Graphics:
Check this out!
http://www.dabs.com/products/gigabyte-ati-radeon-6850-820mhz-1gb-pci-e-hdmi-oc-windforce-2x-7QM3.html?refs=55570000
£120 - amazing for the spec and a free game to boot!
Tower:
http://www.dabs.com/products/best-value-ezcool-h620-case-with-window--no-psu--7QZN.html
£27.99
(It's just a box! Just check a) if you need any extra fans for cooling - an extra £5-£10 if you do and b) the graphics and components will fit in (read all of the component and tower dimensions/size info - some of the GPU cards can be quite bulky))
Hard Drive:
http://www.dabs.com/products/seagate-1tb-barracuda-sata-600-7200rpm-32mb-7C63.html?refs=52780000
£79.99
(1TB HDD, pretty good spec. If it is purely for gaming (not music or videos/films etc) you could get away with one at 320gb and save £15:http://www.dabs.com/products/western-digital-caviar-blue-320gb-s300-8mb-7200rpm-3-5--4H9D.html?refs=56330000-52080000) for the extra money, the 1TB is worth it long-term.
HDMI Cable to plug into Monitor:
http://www.dabs.com/products/cablestogo-2m-velocity-hdmi-digital-video-cable-63NT.html?q=hdmi%20cable
£15
Sound Card:
http://www.dabs.com/products/best-value-5-1-pci-sound-card-via1723-chipset-sc-1723-6LZ8.html
(Dabs.com do a lot of 'value' cards (like Tesco!) won't be the best sound ever but it will do the job nicely-some motherboards already have sound built in so check that too)
£5.80
If you need a mouse and keyboard you can get basic ones for again £5-£10 each
Software:
http://www.dabs.com/products/microsoft-windows-7-professional-with-service-pack-1-64bit-oem--licence-and-media-7GCQ.html?q=windows%207
£108.64
(Windows 7 - use 64 bit to get the most out of your RAM (32bit really only works for 32b) the Home edition is fine. It is always worth checking if you have a copy of this knocking around or you know someone that does)
Grand Total £636 - a bit of savvy shopping* and some time spent on researching components would probably bring that down to £600. I didn't check the link Gothams gave but his graphics card at £100 would save you £20. (On dabs they were £130 so the ATI is a bit cheaper with a free game - I haven't checked the performance of either though so the 460 may still be a better option!)
If you already have a monitor (the link you gave to PC world didn't have one) and / or windows software (Gotham's link didn't include it but the PC World one did). The like-for-like price of a DIY PC is £431 (minus 80 for monitor, 15 for cable and 108 for windows).
The option for the pre-built machine was very good for the money (and windows 7 only £66!) so this isn't to say Gotham was wrong, just that there is another option.
The bonus here is that for similar money as a pre-built one you have the knowledge of building the system and so can upgrade bits as you go along, as games require more memory/faster speeds better graphics you will need to upgrade the system to keep up. You may spend an extra £50 today, but you are saving hundreds over the next few years - in 2 years the pre-built PC's would be close to obsolete - by upgrading components as you go along and as you require/can afford them, you can get 5 years use for the same sort of money, or 2 years use and still have a PC you can use with the newest games/tech.
It is actually VERY easy to build your own PC - components slot into pre-determined slots and cables are all unique. The key is making sure all the components work with each other before you buy. I stress again if you go down this road DO NOT take these recommendations as standard - do some research and ask experts here to confirm all products mesh!
Good luck!
*Use google shopping to search the sites: I have brought from all of these with no problems:
ebuyer.com, dabs.com, amazon.co.uk, overclockers.co.uk
They also do random deals and offers which can save you 10% per component - also check out bundles - sometimes you can save an extra few quid by buying stuff together. It help to order from as few sites as possible so you can get free delivery too.