There's also the confusion as to whether people mean 'Greater London' or 'The City of London'. For the centre of the City, i've generally thought that Leadenhall Market is the centre, given it is built on the original Roman Forum.

For non-Londoners, the city was originally a walled city, and lies to the east end of what is now considered greater london. It's these days synonymous with the financial industry. There are special laws for it, honours like Freedom of the City, it's quite an interesting place.

Although the wall is long gone, there are place names which refer to it, and the gates which exited through it. So we have roads like 'London Wall' and locations like Bishopsgate, Aldgate etc. Newgate was added in the 12th century, so not exactly 'New' these days, so not a very future proof naming convention...

https://leadenhallmarket.co.uk/history-of-leadenhall-market/

https://inspiringcity.com/2013/04/13/the-seven-gates-of-lond...