you have two options for that price. decent but not very upgradable or slightly worst and easily upgradable.
first for not easily upgradable. you can get an A series AMD processor it comes with a pretty decent video card with it. you can play most recent games with very playable frame rates at medium settings at 1280x1024 or so resolution.
http://www.anandtech.com/show/4476/amd-a83850-review/5
you would need the right sales to pull off such a system for £250 more like £300.
my favorite build for absolute budget gaming is with a cheap socket 1155 H61 mobo, a pentium G840 processor(its a touch slower than the i3 2100 and doesn't have quicksync), a 4GB dual channel kit of ddr3 1333, cheapest case power supply combo. which leaves me about £100-£150 for video. then get the best card you can. you should have enough for either a radeon 6850, 6890, 6950 or a GTX 560, 560ti.
you can check here
http://www.tomshardware.com/charts/2011-gaming-graphics-charts/benchmarks,123.html
for performance comparison in games you might care about. keep in mind you will get less frames per second than it shows there since they test with a better processor. but you should get between 70-90% the performance.
if you need to include windows, a monitor, a keyboard and a mouse in that system. then you cant make a gaming system for that money. you would have to drop the graphics card and use intel graphics. which arent horrible anymore but still not very good.
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