"SNIP

For some idea of how the rings would look, here's an ebay listing for some
in the US.
http://cgi.ebay.co.uk/6-5-3-4-MDF-Di...d=p1638. m118

Obviously the almost rectangular bits would be fairly simple to cut with a
coping saw, but I'm a bit stumped about how I'd get a taper with the
rings. Are there any places that'll supply the wood and cut it? I very
rarely do any kind of woodwork, so buying a lot of tools isn't going to
happen, although there is a lathe in the shed that I could use, although I
can't see any way of using a lathe to get a taper...

Using a wood lathe it would be fairly simple. Make a false faceplate from a
piece of MDF. Attach to one side of it a pice of wood which will lift one
edge of the mounted work off the faceplate to the angle of taper you need.

Roughly cut the workpiece circular and mount it on the false plate via
screws in the central waste, with one point on the faceplate and the other
side resting on your previously attached scrap. The back face is now
leaning at the required taper angle, as is the front, but you can now turn
away wood from the front to bring it back parallel with the faceplate,
thereby creating your taper.

Now turn the outside circular and finally part off the ring to the required
diameter from the front.

The work will be a bit unbalnced so you'll need to run the lathe slowly to
avoid vibration.

You can do the same thing perfectly easily on a metal lathe as long as it
will swing the diameter.