Well, quite frankly anything you get for £2500 is going to run everything fine, and £4000 is going to run everything even better. That website you linked to's most expensive prebulit PC is £2100!
That's such a generous budget you won't be facing the issues many have, and can just get the best benchmarked CPU and GPU. Extras will depend on how quite your want your PC to be and will you do more with it than just game?
You really need to narrow down what you want in terms of features and aesthetics. eg. Is running everything at 4k 200 fps important, or will be happy at 1440p 120 fps, or even 60 fps? And how frugal do you need to be? Because your listed budget is 'not at all' at which point we can recommend all sorts of overkill option which will cost you much more and not actually benefit you. It might be that a £1000 PC will suit you perfectly and then you can spend £1000-2000 in a year or two to upgrade it.
I also agree with pharma that PC building forums will probably be more help, but I guess you could always list a spec here for a second opinion.