Hello and welcome to the board.
We may not be as populated as the Glass board but we try to be just as helpful, if not more so.
I'd suspect it's a desk tidy or similar.... for keeping your keys. paperclips and pens in, or it could I suppose be an ash tray of some kind. City of London means the actual City (the square mile) rather than the whole of London, of course.
https://www.cityoflondon.gov.uk/Desk tidies like these were very commonly seen from the 1950s onwards, as pre-war they usually included an inkwell, post-war and into the 1960's the biro was in more common use so an inkwell wasn't needed.
I assume there is no hint of a mark anywhere on the base?