With that in mind i believe having had a quick look at parts it coud be done for £300 although if you have old hard drives and dvd drives kicking around £250 might also be achievable.
The only area that worries me in this type of thing is power. Cheep PSU's are a contradiction. In short they tend to suck so that probably the one area skimping is not allowed. I don't know about you guys but for a cruncher ram is ram, a mobo is a mobo and a case is a case but if your PSU isn't up to 24/7 load then forget it.
So what hardware would you get and why assuming you need to start from scratch?
I'll post mine up later but lets just say a quad core is a must

oh and yeah i might be looking to build a couple of the eventual winners if my payrise comes in....