Original: The style, however, is used when referring to the office as opposed to the holder thereof; thus, "The Rt Hon The Lord Mayor of the City of London" would be correct, while "The Rt Hon John Smith" would be incorrect.
Simplified: The style, however, is used when referring to the office and not to the person; "The Rt Hon The Lord Mayor of London" would be correct, while "The Rt Hon John Smith" would be incorrect.