Having roughly drawn out the system I wanted, I could then look around for places to buy. Given that I'm in Germany, I wanted to also buy the system from Germany in case there was any problem.
Arlt listed some Shuttle systems on their online store, but when I went in to ask them about it they said they couldn't order them any more. Also their monitors were all widescreen apart from tiny 1024x768 screens.
The Computer Upgrade Store advertised fully-assembled K48 systems, with slightly higher specs than I was looking at, with the whole thing (including keyboard and mouse, but no monitor or OS) for 440 euros. Or you can specify all the bits individually from them (for around 390 euros), and for an extra charge (of around 60 euros) they'd also assemble exactly what you want.
Alternate is an online retailer in Germany, and offer a wide selection of components for very competitive prices. The website has a great configuration tool which shows which components are suitable for your system (although the selection changes bizarrely almost daily). They also offer to assemble it for you for about 80 euros extra but offer a 2-year guarantee on the assembled system.
Barebone store offers a similarly large selection of components, and also offer the option of a complete assembly from them.
Harlander offer new and refurbished computer equipment, and this was the only place I managed to find a 1600x1200 Fujitsu monitor. They ran out of new monitors before I was ready to buy but they still had some used ones in excellent condition.
Components of the Shuttle K48 system
The big question was whether to take the easy option of a fully-assembled system or be brave and put it together myself. After getting some advice online (thanks again, tux99!), it sounded like a relatively easy and interesting project, so I took the plunge and ordered the components.
From alternate I got the Shuttle K48, the CPU (Pentium dual-core 5300), the hard drive (Western Digital 640 GB), the optical drive (LG DVD burner) and the RAM (Kingston 2x1GB). I also got a keyboard (Logitech PS/2), a USB hub (Speedstep), and an external hard drive enclosure (2.5", USB for IDE).
In the image, the Shuttle case is on the right (with a blanking plate where the DVD will go and instructions on top), the RAM front left, the hard drive on top of the DVD drive, and the boxed CPU.
From harlander I got the monitor, a 20" Fujitsu 1600x1200 with DVI in. The service from both companies was great and the bits arrived after only a few days.
Now to see if I can put all these bits together!