I can't confirm the game compatibility, not being a PS1/2/3 gamer myself, but on video issue, a large number of U.K. TVs currently on the market will accept 525/60 (American) signals on the direct component video inputs. Many -- but not all -- will also accept NTSC encoded video on the S-video or composite inputs as well, especially the newer LCD and plasma sets. If you have a look in the "Technical Issues" thread there is a lot more about the different degrees of compatibility between the various types of video interconnections.
On the computer power supply issue, most modern PC desktop/tower supplies have a selector switch for 120 or 240V on the rear. It's the peripherals which are often single-voltage only, including all the little "wall wart" units for printers, routers, etc. Quite a large proportion of newer monitors have universal power supplies which will operate on either voltage without adjustment though. The label on the back will say something like "90 to 250V, 50/60Hz" if this is the case.
You could run any 240V-compatible equipment directly from the British supply and just use a smaller stepdown transformer for the 120V equipment if you wish, but you might find it easier to just keep all the computer gear on 120V by bringing a U.S. power strip with you and plugging it into one big transformer.
Do
not use those cheap "transformerless" converters. They appear to be good value for money in terms of watts per dollar/pound, and are much smaller and lighter compared to a similarly rated transformer, but they provide a type of power which can cause problems for electronic equipment. Stick with a simple transformer and you won't go wrong.
http://www.newmarket-transformers.co.uk/http://www.airlinktransformers.com/
