£300 may be a bit tight if you're buying new components.
For starters, have a look here: Build the Best Gaming PC for Any Budget - How To by ExtremeTech
The lowest end system they listed (in July 2010) was for $500US, or about 300UKP. I doubt that the UK purchase price of the parts would have been that little 4 months ago, but perhaps prices have dropped enough since that you could do that. (The Rosewill case is a Newegg house brand, probably unavailable in the UK. There must be equivalents, though.)
It may be more practical to acquire a used system from someone, although it would be much less fun than building one.