Hi there,
May I ask what your current PC spec is? As your graphics card choice will also be affected by the CPU, motherboard, case and PSU you currently have.
For this monitor setup to work you will need a graphics card that can output four display outputs at the same time. You will also want a graphics card with a large amount of VRAM as you will be running games at a very high resolution.
On the AMD side there are quite a few graphics cards that can do this, but you will want to maximise your performance for your money - as such a high resolution will test your systems graphics power to its limits. Therefore, I would recommend something like two HD 7870 2GB cards in crossfire. If you can afford the extra for two HD 7950 3GB cards then even better (though it is over the £600 budget). A single HD 7970 3GB is also an option, it won't offer the same framerates as the crossfire arrangements I mentioned earlier - but you won't have to deal with the issues of running a multi-GPU setup (which include microstutter, spotty support in brand new/old games for crossfire, increased noise and heat).
On the Nvidia side you can either go for a single GTX 680 2GB (
which can output to all four displays at once) or go for two lower-end cards in SLI (for "Nvidia surround gaming"). The GTX 580 1.5GB cards are now under £300 each - so two of these would fit in your budget and generally offer good framerates (though such a setup will also experience similar problems to the crossfire setup I mentioned earlier)- also at such high resolutions teh 1.5GB VRAM may limit performance (with cards running in SLI/Crossfire teh VRAM is not added, but effectively cloned - so there is no VRAM increase when going from one card to two).
Out of all thee options I would probably opt for the GTX 680 as it should offer a playable experience and not come with the issues of multi-GPUs (though you have the option to add a second later on). However, if you are willing to go down the multi-GPU route then a HD 7870 2GB CF setup would be mighty nice.