I looked at building a £500 games box before Christmas, and if you have a monitor and are happy to build yourself then it is certainly possible to make up a very respectable games PC (of course, in the states it was around $750...
).
ISTR I was looking at something like an Athlon 64 3000+, Radeon 9800Pro and a Gig of ram for that money, nothing cutting edge but still not bad and should do fine for what you want. You can spend twice the money on the latest kit, but I reckon it's not buying you much in real performance and personally I'd rather turn the graphics down a notch than spend a grand to get full speed on Far Cry.
Building your own is very simple. It can be a bit more hassle if anything goes wrong, although if you get all the bits from the same place then they should help. Buying the parts from multiple places can turn it into a nightmare of suppliers passing the buck (been there, got the T-shirt...) so don't do that!
edit: 30 seconds searching found a Athlon64 3200+, 512Mb RAM and motherboard bundle for £230 incl. VAT and a 9800Pro for £127, a case for £20 and a 40gig hard disk for £30, that looks good for £400 incl., have I forgotten anything...?