A private Guard Change, anyone?

A Blue Badge colleague was leading a private tour for a family, and included the morning's Guard Change. Aghast at the crowds the mum asked, "Do we really have to stand with all those people over there?" "Yes, " replied the Guide, "I'm afraid so." The mum answered, "So we paid for a private tour and have to stand with everyone else!" What do you think the cost of putting on a private Guard Change might be? Blocking off the traffic + mounted police + flying the Royal Standard + Guards = a million quid?