Wow, that proved a little more difficult than I anticipated.
ft_proposal.xlsA touch over budget when you add a Windows license. I'll let you decide if you want Windows 7 or Windows 8 - just make sure you use 64-bit Windows.
I've included a 3rd-party CPU cooler as the one included with the processor isn't quiet. Perhaps I'm being picky there, but I wasn't happy with level of noise from the CPU fan on a system I built a few weeks ago. If the system is going to be under a desk or something though, then it should be OK, so feel free to lose the Arctic Cooling cooler.
The case is Micro-ATX, so not a full tower. We're down to basic cases with this budget.
I don't know how big a hard drive you want, but I've included a 1TB Black Edition (the fastest you'll get before you go SSD). If you think 120GB would be big enough, or want to carry over a hard drive from a previous system to add more space, then you can get a strong SSD drive for only £10 more - highly recommended. Note that the Samsung 830 is better than the Samsung 840 non-pro.
The cables on the PSU are supposedly quite short, so I've added a couple of extension cables from the PSU to the motherboard and graphics card. The PSU is the semi-modular type though, so hopefully a little easier on cable management.