I wrote CPUs and I meant CPUs.
New GPUs might not be all that interesting. In most games the RTX 2080 is about as fast as a GTX 1080 Ti.
RTX 2080 MSRP = 699$
GTX 1080 Ti MSRP = 699$
The RTX 2070 should be about as fast as the GTX 1080 and guess what, same MSRP at 499$.
MSRP hasn't been announced yet but you can probably take a guess and just looking at the specs the RTX 2060 might be slightly slower than the GTX 1070.
PCPartPicker part list / Price breakdown by merchant
CPU: Intel - Core i3-8100 3.6GHz Quad-Core Processor (£103.72 @ PC World Business)
Motherboard: MSI - B360M PRO-VDH Micro ATX LGA1151 Motherboard (£65.99 @ Amazon UK)
Memory: Team - Vulcan 8GB (2 x 4GB) DDR4-3000 Memory (£78.27 @ CCL Computers)
Storage: Samsung - 860 Evo 250GB M.2-2280 Solid State Drive (£64.76 @ Amazon UK)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive (£29.39 @ Aria PC)
Video Card: PowerColor - Radeon RX 580 8GB Red Devil Video Card (£214.68 @ Amazon UK)
Case: Fractal Design - Focus G Mini (Black) MicroATX Mini Tower Case (£42.96 @ Aria PC)
Power Supply: Corsair - CXM (2015) 450W 80+ Bronze Certified Semi-Modular ATX Power Supply (£47.99 @ Amazon UK)
Monitor: AOC - G2460PF 24.0" 1920x1080 144Hz Monitor (£129.97 @ PC World)
Total: £777.73
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-09-20 20:52 BST+0100
I chose a 580 because the monitor is on sale and got FreeSync. Without that deal expect an extra 70-80£. In that case he could get a different, similar monitor and 580 or 1060 doesn't matter anymore.
Get the 2.5" SATA 860 Evo, it's not listed on pcp UK but should be cheaper than that.
I didn't put much thought into the case so he can change that.
If he wants to spend the rest of the budget he could get a slightly better CPU (i3-8300) and/or 16GB RAM or a significantly better CPU (2600X) that will be of no use to him in most games.
If the monitor deal happens 1070 might actually be doable by shaving of a few pounds here and there. Or just changing the CPU.
https://uk.pcpartpicker.com/list/27CMyX
(remember with the actual SSD price it should be -8£)
B350 mobo could save another 3£ but let's be real here, manually updating the BIOS isn't worth saving 3£.
He could OC it and get about the same performance. He might have to check the QVL for RAM (anything >=2666 is ok) though because those CPU/mobo might otherwise not like it.
I don't recommend going with A320 because either he saves 5£ at the cost of having to update the BIOS and not being able to overclock while keeping 4 RAM slots or he saves 20£ by going with a shit tier 2 RAM slot mobo with the same disadvantages that'll make RAM upgrades more expensive (replacing sticks instead of just adding 2 more) and is truly shit tier.