First of all if you want to play fps games you'll need a good video card. At the point, where you want to put a good video card into a laptop you are already out of the category cheap laptop.
Than as you know games such L4D and CoD need a lot of performance and a lot of performance means a lot of heat for the processor and for the video card. And if you want to keep your computer for a long time you should get the whole thing good cooled. This, in my opinion, is the laptop 's biggest problem: cooling system. A laptop processor generate the same heat as the same processor into a desktop but due to the little place you can't use the same cooling system on a laptop as on a desktop. That means that laptop 's processors often overheat, which means that they get faster older. So if you are planning gaming on laptop you should definitely buy an external ventilator.
Furthermore with a laptop you'll have the problem that you can't upgrade it. If you buy yourself now a relative cheap laptop you won't be able to play the newest games in an year or two.
I myself bought a laptop 3 years ago with the same idea, to use it for gaming and after 2 years of playing WoW I am now not able to run any of the the best games of the past year. So my advise is that you should buy a normal desktop if you are really planning to use it only for gaming.
And still if you want to take a laptop you should keep in mind that some laptops are more expensive than others only because of the name of their trademark. For instance you could find an acer as same as the dell in your link for 50-80 Pounds cheaper.
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