I was privileged to watch this once, and the fabulous sense of a 700 year continuous - "every night without fail" - history adds greatly to the sense of occasion. This is the main exchange:
Sentry: Who comes there?
Chief Warder: The keys.
S: Whose keys?
CW: Queen Elizabeth's keys. (identifying the keys as being those of the current British monarch)
S: Pass Queen Elizabeth's Keys. All's well.
I did ask on the night I was there, but no-one seemed to know. Someone here will, though, so here's the question:
Whose keys were they after Charles 1st was executed?
I think that's a possible answer, as the Tower was/is a Royal Palace. But Charles was in exile, England became a Protectorate, and presumably Parliament held sovereignty and ownership of the former King's property. "The Lord Protector's keys"? "Parliament's keys"?
I've watched this twice from the inside (various organizations eg. Military, Police ) can be invited to watch from inside . I asked the same question and was told Parliament's Keys. When the Yeoman Warders were not there the ceremony was performed by the Garrison and Garrison commander.
Don't suppose you asked him how he knew this did you?
This is really rather interesting because I suspect that it is our equivilent of an oral history tradition. Unless anyone comes up with documentary evidence for this (and that might well not exist) it's very similar to the sort of oral history that you get with pre-literate civilisations.
I suspect that this has been passed down through generations of Yeoman warders and others working at the Tower and has become folklore. Probably impossible to prove or disprove in the same way that the traditions of say aboriginals are