To update what Sarah has written about this event, it commemorates an ancient right held by Freemen of the City of London to drive sheep across the bridge. Back in the day (and we are talking about the mediaeval period when London was a much smaller place), there was only one bridge across the Thames - London Bridge. Anyone who wished to bring livestock into the city from south of the river had to pay a toll. In the absence of other forms of taxation, it was one way that the authorities could raise revenue. Freemen of the City of London were exempt from the charge.
Times have changed, but not the entitlements enjoyed by those who become Freemen. They also have the right to carry a sword within the City of London, although no one exercises the privilege today. For obvious reasons. A few years ago, the annual sheep drive was set up to commemorate the tradition and raise funds for charity. As Sarah says, it should be an enjoyable day, especially as one of our members is participating.
For a bit more information, see this website: https://www.cityoflondon.gov.uk/things- ... drive.aspx