Yes, with just a bit more you have a Ryzen 2700 which has 8 cores and performs extremely well in gaming, better overall than 8600k.
PCPartPicker part list:
https://uk.pcpartpicker.com/list/JzY2bX
Price breakdown by merchant: https://uk.pcpartpicker.com/list/JzY2bX/by_merchant/
CPU: AMD - Ryzen 7 2700X 3.7GHz 8-Core Processor (£273.99 @ Aria PC)
CPU Cooler: Scythe - Mugen 5 Rev. B 51.2 CFM CPU Cooler (£42.95 @ Overclockers.co.uk)
Motherboard: ASRock - Fatal1ty X470 Gaming K4 ATX AM4 Motherboard (£156.46 @ More Computers)
Memory: Corsair - Vengeance LPX 16GB (2 x 8GB) DDR4-3000 Memory (£155.95 @ More Computers)
Storage: *Crucial - MX500 500GB 2.5" Solid State Drive (£76.79 @ Aria PC)
Storage: Seagate - Barracuda 2TB 3.5" 7200RPM Internal Hard Drive (£51.59 @ Aria PC)
Video Card: Zotac - GeForce GTX 1080 Ti 11GB AMP Edition Video Card (£539.28 @ Amazon UK)
Power Supply: SeaSonic - FOCUS Plus Gold 650W 80+ Gold Certified Fully-Modular ATX Power Supply (£89.89 @ More Computers)
Case Fan: Fractal Design - HF14-BK 118.2 CFM 140mm Fan (£15.26 @ Ebuyer)
Case Fan: Fractal Design - HF14-BK 118.2 CFM 140mm Fan (£15.26 @ Ebuyer)
Mouse: Logitech - G703 (Black) Wireless Optical Mouse (£89.99 @ Overclockers.co.uk)
Other: Corsair K63 Wireless Gaming Lapboard for the K63 Wireless Keyboard (£54.95 @ Amazon UK)
Other: Corsair K63 Wireless Mechanical Gaming Keyboard (Cherry MX Red Switches, Blue Backlighting, Ten-Keyless Design, 1 ms 2.4 Ghz Wireless Technology, UK Layout) - Black (£119.98 @ Box Limited)
Total: £1682.34
Prices include shipping, taxes, and discounts when available
*Lowest price parts chosen from parametric criteria
Generated by PCPartPicker 2018-08-01 10:44 BST+0100