Andy,
This used to happen to me every now and again. One of the wires going into the starter got hot (as it was so close to the exhaust primaries) and the solder fractured exposing the contact. When the car got hot the wire would often break contact and not deliver the power to the starter from the battery.
Since getting the work done at the 7 workshop the car stopped doing it, but it sounds like the old problem has crept in again. I think your best bet is to replace the wire (sorry, I can't remember which one it was). I certainly dont think it ring gear.
Superlight no 46
12,000 areroscreen'd miles in 18 months