“Great” back then was a measure of size, rather like “Greater London” with reference to the original London city and the boroughs that were annexed to the city.
The City, as it is called, the one square mile that today is surrounded by “greater” London, only truly became a great city after 1066. . .and mostly through the efforts of the Guilds.
The “Great” in Great Britain was primariliy to recognize its world-wide reach and influence.
The City today is The Corporation of the City of London. The City (run and adminstered by the Guilds) do not run greater London. The City has its own aldermen and a Lord Mayor, and Liverymen of the Guilds vote annually for the sheriff and mayor.