Some other essential trivia:

The place where we stayed is just about on the boundary between the "City of London", and the city of Westminster. Maybe a block or so from where Gordon Brown (the PM) currently resides.

The "City of London" refers to the original, small (2 square mile?), old city from centuries ago, which now includes the port, financial centres, Tower of London, etc.. built on the site of the original Roman walled settlement.

Much of the other interesting bits are in Westminster, with Hyde Park, St.James park, the Palace, parliament (Big Ben..), etc..

The massively huge greater urban area is what us outsiders routinely refer to as "London", but we must be careful to distinguish between "London", and "The City of London" here!

Cheers