What is a good gaming computer for 300 pounds

to be honest I don't think for £300 you can buy all that much in a shop such as tiny or comet etc however that said you may be able to find something semi decent on eBay or I would consider a self build.

the total parts you need are

Processor - Quad or Dual core

Motherboard - just make sure its compatible with yer processor

Memory (RAM) - Don't go below 2Gig DDR2 its not that expensive nowadays
also try buy matched pairs

Hard Drive - start with a 60gig or something you can always buy another

Graphics card - you need something that has 512 but 256 is just, only just good
enough

Case - Personal taste but id go for something in a midi tower n whack an extra
fan in, yeah its noisy but its better than a hot burnt out PC

Power supply - anything above 300 is fine for your price-range

CD drive
DVD drive - I always buy stuff like this separate its cheaper to fix.

Monitor - to save lots of cash buy a CRT monitor they are good but bulky
Keyboard and Mouse

optional extras

Sound-card
Speakers