The pilot reported that during cruise, the engine had a tendency to overspeed when the power lever was retarded but was operating normally at high power. He elected to proceed to the destination with high power set. When power reduction was required for landing a precautionary engine shut down was carried out and a single engine landing was made. Investigation revealed that the concentric control shafts at the fuel control unit were binding and causing mutual interference. The shafts were lubricated and the overspeed defect disappeared. The aircraft had been washed recently. Failure to reapply lubrication after the wash probably contributed to the defect. Significant factors: The FCU concentric control shafts were not lubricated after the aircraft was washed.