The rev counter indicates 500 revs on tick over

What's the color of the smoke? white, white with a blueish color, or black?

could the cruise control auto throttle be engaging ?

Check your igniting system,, and your fuel system

Have you tried disconnecting the battery for 5 to 10 minutes? The vehicle's on board computer should reset without battery power. Its possible you may have to reprogram your stereo radio station presets.

vehicle speed sensor or more commonly a intake gasket vacuum leak.

I have a similar problems on my 2005 9-3. It has developed a number of minor electical issues. including dial and false warning light triggers. I have fixed most of them by simply going round the car disconnecting the electical connectors and spraying "switch cleaner" (Maplin or Radio Shack).
The only problem I have left is the rev counter occasionally starts reading high, removing the fuse (end of dash panel - 4th fuse down) for about 30s with engine off normally resets everything back to normal.
Hope that helps.

Sounds like something is overheating then and possibly a sensor. Not familiar with Rovers but might be a problem with the CAS and/or CPS which tells the ECU the motor is running and when to fire. Also maybe the IAC is bad and when you go from throttle to idle it can't control it and allows it to die.

What was the reason for thermostat replacement? Was it overheating? Are you losing coolant now? Is there oil in the radiator or water in the oil? The white/gray smoke could be a sign of head gasket problems.

The battery could be slightly weak, making the computer go on the fritz, try a fresh battery!!!! The rev counters bounce often with a weak battery.

Leave feedback good or bad.

check the terminal at the back of the alternator prone for loose connection sqeeze it together and refit it.