Hi Bagpuss,
This is a common fault, there are previous posts about it. The water gets in under the plastic strips along either side of the roof, there is a sealed panel joint under the strips and with age the sealant splits slightly allowing in water which runs down unseen from inside the car into the spare wheel well.
It is a very easy fix, just remove the strip (usually the driver's side but could just as easily be the passenger side) and seal it up like you would seal the edge of a bath. I used "Nemesis grabs and seals" from Screwfix which was about £5. There is lots of advice not to use ordinary silicon sealant as it doesn't last. I did mine last spring and it is still fine.
