Building a £300 budget gaming computer?

I know £300 isn't a lot to make a gaming computer, but it is for a young relative of mine who mainly plays Minecraft and some other basic games for younger people. It needs to be Windows 8, so i know that is a chunk of budget gone seeming as it's £80 on Amazon, leaving £220 left over for the actual computer. If someone could help make a custom one even or show me a good basic gaming computer for £300 it would be great!

(Already have a keyboard, mouse, speakers and monitor)
(Not going to download a pirated/free copy of windows 8)
(Needs to be delivered in UK)

Guest

I've made a list from ebuyer.com, all you need to do is copy/paste the 6 digit codes into ebuyers search bar.

Samsung SH-224DB 24X Internal DVD Writer with SATA - OEM 506016 £11.98
Gigabyte GA-F2A55M-DS2 A55 Socket FM2 Motherboard 406371 £38.13
AMD A6 5400K Black Edition 3.6GHz Socket FM2 Processor 398817 £41.50
Corsair 430W CX Builder 80 Plus Bronze PSU 3 Year Warranty 271798£35.82
Antec Case VSK-4000E Tower ATX Black 399300 £27.50
G-Skill 4GB DDR3 1333MHz Memory Module 282306 £29.24
WD 500GB Caviar Blue Hard Drive - 3.5" SATA-III 6Gb/s - 7200RPM 16MB Cache 241715 £40.00
Windows 8.1 DVD OEM- 64- Bit 581064 £75.69

Cart total inc vat: £299.86

Here you go, this should easily handle basic games and minecraft. The processor has built in graphics so there's no need for a separate graphics solution. I've also added a decent power supply, should he need a graphics card upgrade later on down the line.

Hope this helps.

V8VANTAGE