The number of floors is roughly correct for Covent Garden, so I guess it's possible that the original typesetter changed the number of steps, but forgot to change the number of floors.
[1] https://youtu.be/pBTvmrRGlbE?t=516
Incidental anecdote: While searching for this video, which I'd seen a year or so ago, I googled "tube 15 floors sign", but didn't see a reference to it, so I opened YouTube instead, and there, in recommended videos, was a video about the tube... by the same person that made the video above. It was a short hop to find the correct video.
It had never occurred to me that Google personalize youtube searches based on your google searches.
A bit of searching around and I find the building regulations permit a rise per step between 15cm and 22cm. And I find a site which says “A typical rise is 2,600mm, which divides easily into 13 200mm risers, or steps”
I roughly measured the overall height of 8 steps and it was closer to 160cm than 152cm so looks like they are the typical dimensions.
So that, plus a limited number of common ceiling heights, results in a few standard numbers of stairs.
Additionally, building to standards allows you to use interchangeable materials [e.g. 1], decreasing onsite time, which usually directly translates into profit. (Labor is expensive)
It seems reasonable the same has generally been true throughout modern history.
[1] https://www.homedepot.com/p/5-Step-Ground-Contact-Pressure-T...