What case should I use for this gaming build

Solution
The HD 7850 you are looking at is overpriced . You could get a R9 270 which is a similar card and is cheaper.
PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-8320 3.5GHz 8-Core Processor (£101.99 @ Aria PC)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler (£25.24 @ CCL Computers)
Motherboard: Asus M5A99X EVO R2.0 ATX AM3+ Motherboard (£94.99 @ Dabs)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory (£55.34 @ Scan.co.uk)
Storage: A-Data Premier Pro SP900 256GB 2.5" Solid State Drive (£119.02 @ Amazon UK)
Video Card: MSI Radeon R9 270 2GB TWIN FROZR Video...
The HD 7850 you are looking at is overpriced . You could get a R9 270 which is a similar card and is cheaper.
PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-8320 3.5GHz 8-Core Processor (£101.99 @ Aria PC)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler (£25.24 @ CCL Computers)
Motherboard: Asus M5A99X EVO R2.0 ATX AM3+ Motherboard (£94.99 @ Dabs)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory (£55.34 @ Scan.co.uk)
Storage: A-Data Premier Pro SP900 256GB 2.5" Solid State Drive (£119.02 @ Amazon UK)
Video Card: MSI Radeon R9 270 2GB TWIN FROZR Video Card (£132.98 @ Novatech)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply (£46.98 @ Aria PC)
Optical Drive: Pioneer BDR-208DBK Blu-Ray/DVD/CD Writer (£57.26 @ Amazon UK)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) (£64.26 @ CCL Computers)
Wireless Network Adapter: Asus USB-N13 802.11b/g/n USB 2.0 Wi-Fi Adapter (£14.99 @ Ebuyer)
Total: £713.05
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-06-06 23:47 BST+0100)
 
Solution