The Queen's Guard and Queen's Life Guard (called King's Guard and King's Life Guard when the reigning monarch is male) are the names given to contingents of infantry and cavalry soldiers charged with guarding the official royal residences in the United Kingdom. The British Army has regiments of both Horse Guards and Foot Guards predating the English Restoration (1660), and since the reign of King Charles II these regiments have been responsible for guarding the Sovereign's palaces. Despite tourist perceptions, the Guards are not purely ceremonial and are fully operational soldiers.
These soldiers are the best of the best. I watched them at Windsor & Buckingham and they are what you remember, not a building or shrine.