In The Imitation Game in the bits of the film set in the early 1950s, Alan Turing has a primative computer taking up a spare room in his house. Is that a true detail? Would a computer that small & cheap have been technically feasible in 1952?

Haven't seen the film but did it look something like this?

http://en.wikipedia.org/wiki/Automatic_Computing_Engine#mediaviewer/File:Pilot_ACE3.jpg

As this machine, Pilot ACE was running by 1950 then its certainly possible. However such machines were built by research organisations/universities and the electricity requirements would probably had blown a civilian house's fuses and bankrupted Turning. Most early computers had special power lines or personal generators.