IF you don't feel comfortable putting the pieces together and overclocking them, I understand why you'd want to have it done professionally, but if you're going to do that, read the fine print in the little liability form you'll no doubt need to sign to have them do it. If they do not provide a 100% working guarantee and perhaps some sort of a warranty (even for 6 months), then you might as well do it yourself. In other words, if you're paying someone 50-100 quid to "professionally" put it together in the same way you'd do it at home... well, that's money you could put forward to getting a large-enough SSD rather than having a hybrid system or sticking with platters, for instance. Or alternatively, towards PS2's premium membership.
Now, here's the first build I have for you:
http://uk.pcpartpicker.com/p/GoTD
Total before tax: ~880.
Why I chose some of the parts:
First of all, Air cooling is
definitely NOT on its way out. Dedicated cooling systems with external radiators are what can let a CPU go to 5+ GHz, but pushing anything that far will really shoot down your efficiency, not to mention shortens the life of most chips no matter how well they're cooled. I have a close-loop liquid cooler, and although nice, it's not actually that much more powerful than a good air cooler, like the one I have in your build. You're presumably buying this rig in the near future, not several years from now, and in the near future, air coolers will continue to offer superior value. Why would I buy a closed-loop liquid cooler? I travel between my houses and will occasionally bring one of my desktops to the other house, and having the liquid cooler allows the 3-pound radiator to be bolted to the case instead of the delicate motherboard. If you're in a similar situation, you can opt for a closed-loop liquid cooler instead (see build below). Yes, my system is overclocked, but I reached the overclock on the aircooler first, and when I swapped in the water block, the temperatures didn't really drop that much.
A 2500K is not something you should buy today. Ivy Bridge struggles to go as high as Sandy Bridge did because Intel swapped out thermal paste for soldier on the actual inside of the chip, but Ivy Bridge also doesn't need to go as high as Sandy Bridge to deliver the same performance, saving much energy in the process.
At the end of the day, the CM Hyper 212 Evo will get your i5 3570K to 4.3-4.5 GHz just as easy as any closed-loop cooler might. Going beyond 4.5 GHz depends just as much on your luck of the draw and the exact number of defects your piece of silicon has as it does on your cooling.
The GTX 670 is in your build because you stated that first and foremost PS2 is your intended use for this rig, and I think you'll enjoy the PhysX effects (I have them on and they are niiiceee); however, if you're into GPGPU or care about getting the biggest bang for your buck, you can also get a 7970 for 30 pounds more.
The same is true for the -2133 memory, which will help keep your frames much more consistent once you overclock. Personally, I do not recommend going below DDR3-2133 if PS2 is your main intended use.
When you're overclocking, having a very good power supply becomes important. The SeaSonic I have in there isn't modular, but it's extremely well-build and should last through years of torture.
With all that out of the way, I'd found that after a 1 TB HDD, the total was still just above 800 quid, so I threw in an SSD. If you don't need to store much data on your PC, you can put the money from the HDD together with the boot drive to go pure SSD.
Last but not least, the case is largely a cosmetic purchase (the one in the build is the one I personally have). Any case in the 35-50 pound range will satisfy your needs, so pick one that you think looks best.
The website doesn't show anything in the tax column, and I'm not sure what the situation is with VAT over in the UK, so I don't know how much more actual room there is in your budget. But, given some of the above considerations, here are some alternate builds that I can recommend:
Liquid Cooler:
http://uk.pcpartpicker.com/p/Gplc (Total: ~901)
Radeon HD 7970 instead of GTX 670:
http://uk.pcpartpicker.com/p/Gpd6 (Total: ~911)
SSD-only option:
http://uk.pcpartpicker.com/p/Gpix (Total: ~882)