Well, here they provide "packages" where you can buy a chasis and its parts from anywhere between 200 - 500 on the lower end. For a decent one, though it takes about $400 or so.
Wherever you are (I assume UK) go look about and see if its cheaper to buy a second hand computer or its parts (Motherboard, Harddrive, DiskDrive, Processor, Fans, Chasis, Power adapter, graphics card(? To get a cheaper deal. If you want to play games like minecraft (if you aren't the one hosting the server) then a i5 processor, 8GB of RAM and a 250GB harddrive is more than enough to play smoothly (altough it may be out of your price range)
I'm from SG by the way and i'm not sure if you can get one from here but if you do you'd benefit from the conversion rate because pounds to SGD is about 2:1.
The link for the store I got it from will be in the sources
may not be completely helpful but at least you know some specs.
(an i3 processor may make it)