it will be much cheaper if you build it yourself, or have a friend who is tech savvy build it for you..
as for your 350-400 price range, I am not sure of the current exchange rate between the British Pound and the Canadian Dollar, but my roommate recently bought a pretty decent gaming rig for about $899 Canadian..
granted, its not as powerful as most of my home-builts, but it is still powerful enough to run any game currently on the market..
Do you have a PC currently? If so, use the parts that you can from that, and 400 pounds will get you a nice set of parts (mobo/RAM/CPU/Video Card) that you can put in the current case and go. Otherwise, 400 is not going to get you great gaming performance.
Building a computer is very easy, all the connectors can only be plugged into 1 thing the correct way, add a couple of small screws to mount some things and you're done. I'd look videos of people building computers (there are tons) and see if it's something you are willing to do.