Looking for thoughts on my final build. £750 budget for gaming..

Transmaniacon

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Looks pretty good, you might want to drop down to the i5-4570 because it offers better value than the i5-4670. Take the savings get a better PSU and motherboard, and I think the Gigabyte 770 has a better cooler:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor (£142.79 @ Aria PC)
Motherboard: Gigabyte GA-H87-D3H ATX LGA1150 Motherboard (£80.00 @ CCL Computers)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory (£81.88 @ Amazon UK)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive (£42.00 @ Aria PC)
Video Card: Gigabyte GeForce GTX 770 2GB Video Card (£261.29 @ CCL Computers)
Case: Corsair 200R ATX Mid Tower Case (£47.98 @ Amazon UK)
Power Supply: Antec High Current Gamer 620W 80+ Bronze Certified Semi-Modular ATX Power Supply (£79.99 @ Amazon UK)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer (£11.98 @ Ebuyer)
Total: £747.91
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-01-07 18:01 GMT+0000)
 

Transmaniacon

Distinguished
This is an H87 board versus a B85, so it has better features and Gigabyte makes a better motherboard in my opinion. It's not a huge difference, but I tend not to skimp as much on the motherboard.

The Corsair CX power supplies aren't the best quality and some of them have had issues with the Haswell CPUs. That Antec HCG is a better quality product, and more in-line with Corsairs higher-end PSUs.

This is me just nitpicking though, your build will work fine.