Would you have the guts to assemble it yourself?
While it is not hard, by any stretch of the word, you're always better off paying someone else to do it; specially from places like Overlockers.co.uk that offer such service.
Now, to make some assumptions... You will need to replace: PSU, CPU, Motherboard and RAM. You can keep the GPU for the time being and the Case itself.
@Wolfshadw gave a nifty little list of items, but I'd say 16GB RAM and adding a new PSU will bring that up to ~£250. Maybe you can include a good GPU as well and still be under £400...
Let's see...
PCPartPicker Part List
CPU: AMD Ryzen 5 3600 3.6 GHz 6-Core Processor (£187.50 @ Aria PC)
Motherboard: Asus TUF B450M-PLUS GAMING Micro ATX AM4 Motherboard (£82.99 @ AWD-IT)
Memory: Corsair Vengeance LPX 16 GB (2 x 8 GB) DDR4-3200 Memory (£86.98 @ CCL Computers)
Power Supply: Silverstone Strider Essential 600 W 80+ Bronze Certified ATX Power Supply (£55.47 @ Scan.co.uk)
Total: £412.94
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-08-27 14:01 BST+0100
Cheers!