Thanks for the additional advice. I was planning to make a capacitor out of foil and newspaper interleaved. One day when I've finished all the other things I want to play around with...
http://www.crystalradio.net/crystalsets/hassell/index.shtml
Newpaper will be 'fun' to work with as its moisture content will vary with environmental conditions, making its dielectric constant not very..erm..constant - unless you impregnate it with wax or a lacquer.
(Made plenty of crystal sets during my teen years in the mid 70s-80s)
I have a "crystal" radio (uses a modern diode) all built on a paper towel tube. The coil is wound on the tube like usual but at the other end of the tube there's also a layer of foil and a smaller tube with a layer of foil that slides inside that to make a variable capacitor.
Also, I find that inserting a ferrite rod into the coil (or winding the coil around the ferrite rod to begin with) makes tuning much more effective (sharper) and makes the audio signal much stronger. A steel or iron 6" nail also works if you want to dispense with the ferrite rod.
I made a single transistor regenerative set next and because the local BBC signal was so powerful I literally didn't even need an antenna at all!
Another single transistor was all that was required to drive a speaker loud and clear.