Why does your rover 400 cut out when warm and then not start again?

I don't have a rover 400, but...

I had a similar issue with a 1984 Ford Escort a little over 10 years ago that turned out to be some module attached to the side of the distributor. It cost me about $35 and was very easy to remove and replace. I can't recall what the module was called, but I know it wasn't a voltage regulator, or the coil.

If you can, add some more information about the vehicle and a better answer could probably be provided.