Why does fan keep running after engine turned off temp gauge rising almost to red on rover 214?

The fan continuing to run after turning off is normal it just proves how hot the engine is getting (overheating). Your promblem is why is it overheating? Being a 214 I would suspect head gasket but it could be a coolant circulation problem (thermostat failed in closed position, water pump worn, or simply a partially blocked radiator) If it isn't the head gasket it soon will be if you don't sort it on this engine.