From much of England's history, the Lord Mayor of London conducted municipal business out of their home or guild hall. Only in the aftermath of the Great Fire of 1666 did the idea come about to build a residence for all Lord Mayors. Not all of them at once, mind.
A house full of Lord Mayors. That's a reality show waiting to happen.
The architect George Dance the Elder, then the Clerk of the City's Work, was hired to design and build what would be called the Mansion House. Construction began in 1739 and the House wasn't completed until 1758. The first Lord Mayor to move into the Mansion House was Sir Crispin Gascoigne in 1752, while the House was still under construction.
Today, the Mansion House serves as the Lord Mayor's residence and office as well as a site for business meetings and city functions, including the annual "Mansion House Speech," where the Chancellor of the Exchequer speaks on the state of the British economy.