Distance is measured from Charing Cross.
The Cross is near Nelson's Column, but I would be surprised if the column was actually the central point.
As others have pointed out, this leads to some weirdness, as lots assume that the City (old London & older Roman London) would be the obvious place to measure things from.
Which is also where the A1, A7, and A8 meet.
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...
You can still see chunks of the wall: https://livinglondonhistory.com/londons-ancient-roman-and-me...
https://www.londonmithraeum.com/
Free to enter, but pre-booking recommended.
https://www.quora.com/Does-the-City-of-London-as-it-is-defin...
That would be the centre of the City, but not necessarily of the city.
E.g. Waterloo Station would be considered South London but is actually at the same latitude as Buckingham Palace!
Hence why a Londoner would never describe Vauxhall as "Central".
Londoners would generally discount any part of this map south of the river from "Central London":
https://en.wikipedia.org/wiki/Central_London#/media/File:Ope...