Agreed, there is no such thing as a cheap gaming machine! the cheapest your going to get a half decent gaming machine for is around £400-£700 and of course build it yourself, if your looking to just buy a pre built tower, dont expect much performance from it! This is going from personal experience, i went to pc world when i was younger paid about £900 for a pc package to later find out i could have built it myself for half the value or if you like have a machine atleast twice the performance for the money i spent.
Good luck anyhow