I need a desktop that can play games reasonably well for under £750. It needs to be small because I don't have much space and I need to move it from location to location. I was considering a gaming laptop, but I don't have the money for one.

Or if you could recommend a small desktop whose GPU I could upgrade, that would be helpful as well.

First of all are you looking to buy a pre-built computer, or are you willing to make your own?

For $1500 you can build a decent gaming rig...for example:

P35 mobo
E6750
2GB DDR2 800 Ram
8800gts
320Gb H/D
DVD burner
corsair hx520
mouse/keyboard
speakers
case
O.S.

And still have some spare change leftover.

Ok, what kind of physical size are you looking for? Also, do you need a screen (LCD I assume) included in that £750?

ibleet, you need to factor in that electronics in the uk are more expensive that sort of build isn't really possible for that price. I'd maybe suggest a shuttle or midi tower if you want portability really.

For $1500 you can build a decent gaming rig...for example:
P35 mobo
E6750
2GB DDR2 800 Ram
8800gts
320Gb H/D
DVD burner
corsair hx520
mouse/keyboard
speakers
case
O.S.
WHAT???? u guys are in heaven in the USA, in the UK everything muchmuch more!

tha's like 3k us so 8800gtx and q6600 with ddr2 800 ram i recommend pc&c 750w. gaming mouse g15? get a good airflow case like tt armor

apevia xqpack-2 small micro atx lan box
8800gt seems to be the best bet thus far, releases soon if not already.
to save dough i would buy an amd proc based on am2 platform
m2npv-vm from asus isn't a bad micro atx motherboard
if you want to overclock, get an amd 2.6 dual core black edition
if not i'd just buy an amd dual core 2.8. paired with some ddr2 memory
(integrated memory controllers are better, but they only run memory at full speed on certain frequencies, so 2.4 or 3.2, 2.8 works as well.

the black edition will oc up to 3.2 stable, supposedly... not sure about on that mobo. anyway, have fun one way or another. and make sure to get a psu with 2 12v rails (that case i mentioned comes with one), cuz most mid/high end graphics cards require more than 20 amps and the standard for "safe" operation on a 12v rail is suggested to be 18A or less... i think. anyway, get 2 12v rails and i think you'll be ok... about 60 bucks should get ya a new one... what's that like 30 pounds?

good luck, i'm doing the same build up right now, only i'm pushing mine under 700 us dollars... and wanting to play games... oh and in European psu's has a pfc or some crap, i dunno, i didn't read into it because it didn't apply to me... so look that up (forums, psu's, and it should be the first/main post, read that, lots of good info)

ps... really, find that psu faq... it will save you soooo much time and money! I realized that i bought a psu for a pc that would technically last 20 years under normal operation... i could have saved 20 bucks or more... or the other way around... if your pc sucks down 480 watts at full load, and you've got a 500 watt psu and all that jazz... after a while it will fault because it loses output power over time... anyway... read that faq. it's more about psu's than you will ever want to know.