£300 gaming pc

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor (£48.38 @ Amazon UK)
Motherboard: ASRock H81M-HDS Micro ATX LGA1150 Motherboard (£36.97 @ CCL Computers)
Memory: Kingston HyperX Fury Black 8GB (2 x 4GB) DDR3-1333 Memory (£39.25 @ Amazon UK)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£39.99 @ Amazon UK)
Video Card: Gigabyte GeForce GTX 750 Ti 2GB WINDFORCE Video Card (£97.99 @ Amazon UK)
Case: NZXT Source 210 (Black) ATX Mid Tower Case (£32.65 @ Scan.co.uk)
Power Supply: EVGA 430W 80+ Certified ATX Power Supply (£29.99 @ Scan.co.uk)
Total: £325.22
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-07-11 12:18 BST+0100

This build is slightly over you budget, but it is a great build with upgradable parts if you'd like, however it does not include an OS, if it needs to be cheaper just say so.
 
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