£300 you can build an ok gaming pc yourself, you will save a lot compared to pre built and can use that saving for extra performance. No point buying a pre built gaming pc at this price point. Heres a quick 'taster' of what you can do for £300 yourself!
http://uk.pcpartpicker.com/p/B3FzhM
This is the best build for £300 I can think of, I left out an aftermarket CPU cooler which you can always upgrade later.
If you are concerned about PC building too 'difficult' or 'too hard', thats the number 1 mistake. There is a whole world waiting for you. Believe me!