I don't have any idea how much it would cost especially in the UK but I'd say don't discard buying a second hand PC. I bought an used HP workstation with dual Xeon (yep 2 processors, 12 physical cores) with 24gb RAM, built in RAID (2 bays) and a not so good GTX 750ti for 950 AUD and it works great.
I hadn't tried it for games until this week because it I got specifically for photo and video editing and I was told that the graphics card wouldn't be that fast for gaming. But now with this Steam sale I went and got Assetto Corsa, pCARS, Raceroom (just a couple of tracks) and I'm really surprised how well they all run @1080p, especially pCARS comparing it to the XBone version.
Please note that I could have gotten something a lot cheaper like a used PC with an i5 and then spent the difference of a new PC on a more powerful GPU, if it's mainly going to be used for gaming I'd suggest having a look for something like that. You won't believe the kind of bargains you can find on the ol' Gumtree, There's a UK site too, right?