£500 Budget Gaming PC

I need a new LAN PC and I have a budget of £500.

I require it to be as small as possible so it can fit nicely in tight corners.

I don't require an OS, monitor or peripherals as I will buy them further on.

Thanks in advance.

What games are you looking to play?

Battlefield 4, Thief, Arma, Call Of Duty etc.

http://uk.pcpartpicker.com/p/34557

I would build something like this. The motherboard has wifi, which might be helpful - but wifi is never ideal. There's £50-ish remaining, and you might use that to purchase an aftermarket heatsink or an SSD.

Suggestions:

http://uk.pcpartpicker.com/part/noctua-cpu-cooler-nhl9a

http://uk.pcpartpicker.com/part/a-data-internal-hard-drive-asx900s3128gmc

It should play Battlefield 4 multiplayer on ultra presets 1080p