Hi!
If you want a working system bought entirely new, you'll have a really bad time because just the cost of the OS is 1/3rd / 1/4th of your budget unless you buy it on Kinguin or other 3rd party sites. I would suggest you go for used parts in this case because you can get way more performance than new, I am not from the UK myself so I have no idea what you have in your country but I did put up a system with I7 3820 watercooled, GTX 970 for aprox £550. If you look around on Ebay for used parts you can get a monster PC with GTX 770/780, I5 4th gen, maybe i7 2nd gen (i7 2nd gen is better in multicore). But remember it takes patience and time to find the correct parts and always try to compare. If you however want to build entirely new...