PCPartPicker Part List:
https://uk.pcpartpicker.com/list/tTkfQZ
CPU: AMD - Ryzen 5 2600 3.4 GHz 6-Core Processor (£135.97 @ Amazon UK)
Motherboard: MSI - B450 Gaming Plus ATX AM4 Motherboard (£84.89 @ Box Limited)
Memory: Corsair - Vengeance LPX 16 GB (2 x 8 GB) DDR4-3000 Memory (£75.99 @ Aria PC)
Storage: Western Digital - Blue 1 TB M.2-2280 Solid State Drive (£86.49 @ Amazon UK)
Video Card: ASRock - Radeon RX 570 8 GB Phantom Gaming X Video Card (£125.63 @ More Computers)
Case: Corsair - 100R ATX Mid Tower Case (£45.73 @ Amazon UK)
Power Supply: Corsair - CXM (2015) 450 W 80+ Bronze Certified Semi-Modular ATX Power Supply (£48.48 @ Amazon UK)
Total: £603.18
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-05-05 16:04 BST+0100
6 core / 12 thread CPU, air cooler is included, should be able to hit 3.9-4.0 GHz.
Motherboard is nothing to go crazy about, but good enough.
RAM could be a bit faster, especially the timings, but DDR4-3000 is a good price/performance compromise. Especially at that price.
Good storage capacity: 1TB SSD isn't common at that price range. I'd buy a sata 6 SSD down the road to expand it though.
Graphic Card is good enough for modern AAA games at 1080p/60 and medium-high settings. 8GB is a must do imo.
PSU isn't awfully powerful, but it is a well known brand and 80+ bronze is appreciated at that price range.
£4 over your max limit, but I wouldn't give up on 8gb of video ram, 1TB of SSD storage or get a worse CPU because of it. If you want get a cheaper case.