your question is too general. There are MANY magazine articles that appear monthly on what you want to do. If you're building it for general purpose use, you can build a simple tower for dirt cheap and under $500
"Cheap as possible" is a bit too general, some people consider £300 to be cheap, others may think £700. So you have to provide at least some sort of a price range, and if that price range includes peripherals/monitor.
As you are in the UK some good places to start would be ebuyer, aria, overclockers.
By my calculations that comes to £454. Notice there isn't a hard drive included in that build, prices are still very high at the moment die to the Thailand floods so if you have an existing one you can re-use that. Also I've just picked the components from one website so you might be able to get better deals if you shop around.
If your budget will stretch, you can get this 6950 graphics card for £199, it might even unlock to a 6970 and will run pretty much everything you throw at it.