fan running on after engine turned off, could this be a faulty thermostat
Fan speed controller or relay is possible. Speed controllers known issue.
Check ECU wiring for water ingress in Plenum chamber.
There is a fan on the autobox cooler hidden in front wings that is also a known issue.
Perfectly normal on some cars, Golf I had would switch fan on after I had locked the car and was walking into the house.
No idea if its normal on a Rover, what was?