Again Trailspotter, you're just putting forward your own theory. Although the
City and the
Monarchy themselves state this ceremony is about the monarch asking permission to enter the City, you choose to ignore that, and claim it's just about the Mayor signifying his loyalty.
At Charles and Diana's wedding, the Mayor meet the monarch on the steps of St. Paul's, as his successor would do 31 years later on the Diamond Jubilee. The ceremony of the monarch touching the Pearl Sword happened on the step's of St. Pauls.
Can you find a video of the Queen arriving in the City without having to touch the Pearl Sword?
Actually, I have asked myself a different question: how many times the ceremony of touching the Pearl Sword was re-enacted during the Queen's 60-year reign? It should be a very public event each time, that would attract many royal watchers, so there would be a plenty of videos or photos, right? Well, it is quite opposite. I have found only four such events: Silver Wedding Anniversary, Golden and Diamond Jubilees and Royal Wedding of Charles and Diana. In the former two events the touching ceremony was at Temple Bar:
http://www.youtube.com/watch?v=Hg_cadCg-2s
http://www.youtube.com/watch?v=QftRZ3pGqC8
There was no second touching at the St Paul's steps in those two events. In contrast, there was no stopping at Temple Bar in the latter two events, the Sword was presented to the monarch at the steps on her arrival to St Pauls.
EDIT: There is a video of fifth event from 1954. It probably was her first touching the Pearl Sword (at Temple Bar):
http://www.britishpathe.com/video/londons-city-welcomes-queen/query/15601
There must have been other occasions when the Queen visited St Pauls, for example, her Silver Jubilee, but I could not have found a photo or video record of the touching ceremony being perform.
EDIT: There is a
newspaper report of the touching ceremony at Temple Bar.
So far, regardless of the places where the touching ceremony was performed, all records show, as pointed by MikeC, that
the Lord Mayor symbolically presents the sword to the Queen to show his subservience to her authority, but they show nothing to suggest that the Queen is actually asking his permission to enter the City.
Anyway, these were the state events, involving official processions, state coaches, cavalry escort etc. Apart of them, the Queen has been doing hundreds official public engagements every year, visiting many places of her realm, including the City of London, like, for example:
http://www.youtube.com/watch?v=6TeFtAzDxiI
There is nothing on the record to suggest that any of her public engagements in the City has begun with her touching
the Pearl Sword.