Gaming PC Build for £700-£850

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor (£164.39 @ Aria PC)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler (£25.45 @ Scan.co.uk)
Motherboard: Asus Z87-A ATX LGA1150 Motherboard (£103.04 @ Scan.co.uk)
Memory: Corsair Vengeance Pro 8GB (2 x 4GB) DDR3-2133 Memory (£66.64 @ Ebuyer)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£42.73 @ Aria PC)
Video Card: Asus Radeon R9 290 4GB Video Card (£317.99 @ Aria PC)
Case: Corsair 200R ATX Mid Tower Case (£45.90 @ Amazon UK)
Power Supply: XFX 750W 80+ Bronze Certified Semi-Modular ATX Power Supply (£69.78 @ Amazon UK)
Total: £835.92
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-20 22:19 BST+0100)
 
AMD build with a SSD
PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-8350 4.0GHz 8-Core Processor (£133.99 @ Amazon UK)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler (£25.45 @ Scan.co.uk)
Motherboard: Asus M5A99X EVO R2.0 ATX AM3+ Motherboard (£94.31 @ Amazon UK)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1866 Memory (£63.91 @ Amazon UK)
Storage: Samsung 840 EVO 120GB 2.5" Solid State Disk (£59.95 @ Amazon UK)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£42.73 @ Aria PC)
Video Card: Asus Radeon R9 290 4GB Video Card (£317.99 @ Aria PC)
Case: Corsair 200R ATX Mid Tower Case (£45.90 @ Amazon UK)
Power Supply: XFX 750W 80+ Bronze Certified Semi-Modular ATX Power Supply (£69.78 @ Amazon UK)
Total: £854.01
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-20 22:25 BST+0100)
 

+1, the 290 will handle anything you throw at it.