Pre-built no way, there is nothing for sale that in any way, shape or form could be considered a gaming PC. If you're lucky you will get a "nettop" or ultra low end PC with low end integrated graphics.
I priced up some parts, and I reckon you can put together a system based on AMD's A8-7600 APU with 4Gb DDR3-1866 for about £230 without making too many sacrifices on quality. I refuse to suggest an own brand £10 PSU or a £20 case with included "500 w PSU" in it that lots of retailers sell, as they are quite simply poor quality and I don't believe this is the right area to save money. The A8-7600 has reasonably powerful on chip graphics and 4 CPU cores, and should be capable of running a lot of current games at medium quality settings. 4Gb is below ideal levels (8Gb far more comfortable) but it's all you can afford. The other nice thing about the A8-7600 is that in future you can upgrade to dual graphics with a low cost R7-240 or R7-250 GPU and according to the tests linked above, that can bring large FPS improvements. Example part list - http://uk.pcpartpicker.com/p/7Yjkqs
Then there's used or refurbished PC's but obviously the deals are highly variable and many of them are ex-office PC's and quite unsuitable for games..
Edited by jonuk76, 22 September 2014 - 06:33 AM.