PCPartPicker part list:
https://uk.pcpartpicker.com/list/49dQJV
Price breakdown by merchant: https://uk.pcpartpicker.com/list/49dQJV/by_merchant/
CPU: Intel - Core i7-7700 3.6GHz Quad-Core Processor (£263.00 @ Amazon UK)
Motherboard: Gigabyte - GA-B250M-DS3H Micro ATX LGA1151 Motherboard (£60.95 @ Aria PC)
Memory: Team - Dark 16GB (2 x 8GB) DDR4-3000 Memory (£119.99 @ Overclockers.co.uk)
Storage: Seagate - FireCuda 2TB 3.5" 7200RPM Hybrid Internal Hard Drive (£84.84 @ Aria PC)
Video Card: Gigabyte - GeForce GTX 1080 8GB WINDFORCE OC 8G Video Card (£492.90 @ Alza)
Case: Cooler Master - MasterBox Lite 5 ATX Mid Tower Case (£39.98 @ Ebuyer)
Power Supply: SeaSonic - S12II 620W 80+ Bronze Certified ATX Power Supply (£59.99 @ CCL Computers)
Operating System: Microsoft - Windows 10 Home OEM 64-bit (£85.20 @ CCL Computers)
Total: £1206.85
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-08-19 20:21 BST+0100
Had to skimp on a few things to get the price right. I had to go with a cheaper motherboard, 7700 instead of 7700K, used stock cooler, didn't get an SSD but got a Hybrid drive instead, went with a GTX 1080 instead of a GTX 1080 ti, and I got a cheap case.
It should play games at 4K though pretty well with some settings lowered.