Cheap gaming pc in Cooler Master elite 130

Solution
Well then... This is what I came up with:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Celeron G1820 2.7GHz Dual-Core Processor (£26.44 @ CCL Computers)
Motherboard: Asus H81I-PLUS Mini ITX LGA1150 Motherboard (£49.38 @ Amazon UK)
Memory: Corsair 4GB (1 x 4GB) DDR3-1333 Memory (£23.00 @ Dabs)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£39.50 @ Amazon UK)
Case: Cooler Master Elite 130 Mini ITX Tower Case (£37.82 @ CCL Computers)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply (£46.98 @ Aria PC)
Optical Drive: Lite-On...

RazerZ

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PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Pentium G3220 3.0GHz Dual-Core Processor ($58.99 @ Amazon)
Motherboard: ASRock H81M-ITX Mini ITX LGA1150 Motherboard ($65.38 @ Newegg)
Memory: G.Skill Sniper Series 4GB (1 x 4GB) DDR3-1600 Memory ($36.99 @ Newegg)
Storage: Western Digital Caviar Blue 320GB 3.5" 7200RPM Internal Hard Drive ($37.48 @ Amazon)
Video Card: PowerColor Radeon R7 260X 1GB Video Card ($69.99 @ Newegg)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($26.99 @ Newegg)
Total: $295.82
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-06-02 09:22 EDT-0400)

You could also upgrade the CPU to an i5 later on. This should make for a decent budget gaming pc.
 
Well then... This is what I came up with:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Celeron G1820 2.7GHz Dual-Core Processor (£26.44 @ CCL Computers)
Motherboard: Asus H81I-PLUS Mini ITX LGA1150 Motherboard (£49.38 @ Amazon UK)
Memory: Corsair 4GB (1 x 4GB) DDR3-1333 Memory (£23.00 @ Dabs)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£39.50 @ Amazon UK)
Case: Cooler Master Elite 130 Mini ITX Tower Case (£37.82 @ CCL Computers)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply (£46.98 @ Aria PC)
Optical Drive: Lite-On iHDS118-04 DVD/CD Drive (£10.78 @ Scan.co.uk)
Operating System: Microsoft Windows 7 Professional SP1 (OEM) (64-bit) (£59.00 @ Amazon UK)
Total: £292.90
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-06-02 14:30 BST+0100)

You'll have to get a dedicated GPU later for a decent gaming experience. I also recommend adding another stick of RAM and upgrading the CPU when you have the money to do so.
 
Solution

Upgrade to a dedicated GPU later (even if you have a cheap GPU it will still run better) and upgrade the CPU later. +1 to this awesome build for the budget!