UK Car Repair: Rover 45 Connosseur - engine stutters, loss of acceleration, fuel vapour, rover 45

Question
If I switch off the ignition and then restart the engine after a short period  of less than 10 minutes, my engine starts to cut out after I driven the car for about a mile. My local garage suggested that this problem may be due to a sticking valve and advised me to use cleaning additives in the petrol and the oil. I have tried both cleaning methods with no success and am not convinced that this may be the cause of the problem. Could you please advise.  

Answer
Am I to understand that if you restart it after a longer period it is fine?  How many Km's are on the car? This type of problem makes me suspect a problem in the evaporative loss system.  This is the control system that collects the fuel vapour from the tank and then collects it until it can be reintroduced to the engine.  Some systems will apply a vacuum to ensure fuel cannot flow and, they are heat related. Perhaps you could temporarily disconnect the system -there should be a fuse- and then try it!