Best build under £1,500

This should be decent. It includes the OS. I tried fitting in a 1080Ti, but that would require cutting down the 8600k to an 8400:
PCPartPicker part list: https://uk.pcpartpicker.com/list/bjMXXH
Price breakdown by merchant: https://uk.pcpartpicker.com/list/bjMXXH/by_merchant/

CPU: Intel - Core i5-8600K 3.6GHz 6-Core Processor (£243.79 @ Alza)
CPU Cooler: Cooler Master - MasterLiquid 120 66.7 CFM Liquid CPU Cooler (£50.47 @ Amazon UK)
Motherboard: MSI - Z370 SLI PLUS ATX LGA1151 Motherboard (£126.49 @ Scan.co.uk)
Memory: Corsair - Vengeance LPX 16GB (2 x 8GB) DDR4-3200 Memory (£142.98 @ Ebuyer)
Storage: Samsung - 850 EVO-Series 250GB 2.5" Solid State Drive (£82.10 @ Amazon UK)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£37.79 @ Aria PC)
Video Card: EVGA - GeForce GTX 1080 8GB Superclocked Gaming ACX 3.0 Video Card (£517.92 @ CCL Computers)
Case: NZXT - S340 Elite (White) ATX Mid Tower Case (£72.96 @ Aria PC)
Power Supply: Corsair - RMx 750W 80+ Gold Certified Fully-Modular ATX Power Supply (£99.96 @ PC World Business)
Operating System: Microsoft - Windows 10 Home OEM 64-bit (£86.82 @ Aria PC)
Total: £1461.28
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-12-30 16:18 GMT+0000

With the 8700k, you go 65 pounds over budget, but this can be reduced if you remove the OS:
PCPartPicker part list: https://uk.pcpartpicker.com/list/jGFCBP
Price breakdown by merchant: https://uk.pcpartpicker.com/list/jGFCBP/by_merchant/

CPU: Intel - Core i7-8700K 3.7GHz 6-Core Processor (£347.94 @ Aria PC)
CPU Cooler: Cooler Master - MasterLiquid 120 66.7 CFM Liquid CPU Cooler (£50.47 @ Amazon UK)
Motherboard: MSI - Z370 SLI PLUS ATX LGA1151 Motherboard (£126.49 @ Scan.co.uk)
Memory: Corsair - Vengeance LPX 16GB (2 x 8GB) DDR4-3200 Memory (£142.98 @ Ebuyer)
Storage: Samsung - 850 EVO-Series 250GB 2.5" Solid State Drive (£82.10 @ Amazon UK)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£37.79 @ Aria PC)
Video Card: EVGA - GeForce GTX 1080 8GB Superclocked Gaming ACX 3.0 Video Card (£517.92 @ CCL Computers)
Case: NZXT - S340 Elite (White) ATX Mid Tower Case (£72.96 @ Aria PC)
Power Supply: Corsair - RMx 750W 80+ Gold Certified Fully-Modular ATX Power Supply (£99.96 @ PC World Business)
Operating System: Microsoft - Windows 10 Home OEM 64-bit (£86.82 @ Aria PC)
Total: £1565.43
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-12-30 16:19 GMT+0000