It’s doable…
I picked up a refurb HP Z230 Tower (you don’t want the mini form factor) with an i7-4790 processor and 16GB of RAM and a 120GB SSD recently for £160. I picked up a nearly new Gigabyte 1060Ti 6GB gfx card for £150 it and it’ll play virtually anything at high frame rates at 1080p! It’ll play many games at decent frame rates at higher resolutions than that, but will struggle with the latest games on 4K… But it’s a staggeringly powerful machine for just over £300!
In fact, I only really picked it up on a whim, don’t really use it at all. My GF’s lad is big into PC gaming and I thought I’d have a go again, have switched it on maybe 3 times in the last 3 months! Drop me a line if it’s of interest…
Just for reference, it scored a geekbench score of 13364, scored approx 750 in Cinebench CPU test, and scored just shy of 100fps in Cinebench 3d gfx test… OK these numbers wouldn’t worry a current i7 machine with dual 1080’s in, but for £300 it’s lightning fast!