I see the AMD spend thrifts are out in force.
For what you want, on your original budget a 2nd hand i5 4670K @ £100-£125 or less if your lucky is your best bet and a lot less hassle.
With Ryzen not only would you need need a new Mobo, but ram and a new PSU to run it. (i7 would probably be too much with an RX4/580 on the CX430)
Costs keep mounting up and your not going to get much more performance with Ryzen on the games you mentioned. (If any at all)
And a RX 480 8Gb 8000Mz £210
https://www.overclockers.co.uk/giga...ddr5-pci-express-graphics-card-gx-18d-gi.html
Main reason for 480 over 580 is you PSU will be getting close it it's limit with a reasonable margin. It could run an RX 580, but certainly a lot closer to it's maximum output.