London used to have a similar system for distribution of mail throughout the city, officially known as the London Post Office Railway, or Mail Rail. I heard there were plans to open up some of the stations and tunnels to the public, not sure what they came of them though.

https://en.wikipedia.org/wiki/London_Post_Office_Railway

I used to work in Royal London House in Finsbury Square and the lowest subterranean level was sealed up but Royal Mail branded; given that it was a stones throw away from Mount Pleasant, I always wanted to gain access and see if it had access to Mail Rail or was even a station.