I don't tend to re-read books, but I have a fantastic book by a write called Christian Wolmar, called the Subterranean Railway.
It is fantastic, which I don't say lightly, covering the whole history of LU from before and beyond, and I think i'm right in saying (another reason why I have to re-read, my memory makes a collander look like a saucepan) it covers all of the lines and their preceding incarnations. Here's a link:
https://www.amazon.co.uk/Subterranean-Railway-Underground-Changed-Forever/dp/0857890697/ref=sr_1_3?keywords=london+underground+history&qid=1570267319&sr=8-3
Hope that helps, and apologies if I am barking up the wrong tree with that - it might not be specific to what you asked for, but you'll come out knowing all sorts of things you didn't know or didn't even know you wanted to know!