700 euros? That can be done.

Unfortunately, you'll get ripped off my European retail prices. The "Summer GPU Wars" are about to start too--nVidia and ATI will probably get on a releasing spree... meaning that current high-end will lower in price and new high-end will appear. I'm personally going to stay tune to the ATI HD4000 series of cards--the HD4870, to me, is an interesting card. That, and RV700 will be a multi-GPU design, and rumor has it, with hard-wired CrossFireX (including a shared memory pool).
Point of View GeForce 8800GT 512MB, £106.98
or
GeCube Radeon HD3870 512MB, £104.99
Gigabyte GA-EP35-DS3R, £74.95
Windows Vista Home Premium 64-bit OEM, £62.96
Corsair XMS2 4GB (2x2GB) DDR2 800, £69.99 (because I cannot and will not recommend OCZ. And boy! I can easily buy the same amount of memory for sub-$60 USD!)
Cases... I selected Case 2 and 3 myself, but that's because I own one and it's "average" among the 7 listed for you. 40.19 euros factored in.
Generic brand in red with large side fan, LED screen, questionable quality?, £23.99
Same as previous, but in black, £23.99
XClio/Aplus 188AF, £31.08 (I own one of these--great cases for the money and cooling!! I don't use this particular case, as my super heatsink tower just won't fit, but I still own it and have worked in it and its brother!)
XClio/Aplus Propeller, £40.19 (I own one of these too--more space but it's the same basic design as Case 2. This is what I have my rig in--it's a nice case and there's a good amount of space in it too, for routing cables.)
Antec 300, £37.99 (This Antec Three Hundred is new and I hear it's a real pleasure to work in! Seriously--great from what I hear!)
CM Centurion 5, £34.98
CM Stacker 690, £49.99 (This CM690 is a very nice case from what I hear, but may be out of budget)
Power supplies... I selected the Seasonic S12 II 500W, since it's an excellent unit and *actually* worth the price!
Seasonic S12 II 430W, £44.64
Seasonic S12 II 500W, £52.75
Corsair 520W HX (modular), £63.23
Corsair 620W HX (modular), £82.98
Hard drives... I would select the WD 500GB model, personally
Western Digital Caviar SE16 320GB, £40.74
Western Digital Caviar SE16 500GB, £53.80
Lite-On 20x SATA DVD+/-RW/RAM with 3 bezels and Nero, £20.49 (I have on of these too, but an OEM black version)
Now what? Just processor (and cooler, and TIM, and TIM remover) I think... I left the processor for last because that's where you want to "splurge". So, here goes! (wait for my edit)
Arctic Cooling MX-2, £3.27 (TIM)
Arctic Silver ArctiClean, £4.00 (TIM remover)
Coolers...
Scythe Mugen (Infinity), £32.68
Scythe Zipang, £34.26
Zalman CNPS9700 LED, £34.76
Processor time!
Intel Core 2 Duo E8400 (3GHz and new Wolfdale), £124.99
Intel Core 2 Quad Q6600 (2.4GHz and older Kentsfield), £137.95
Done. That should come out to ~£700.