Transport for London have a clear policy. You need a permit for commercial photography/filming, you can hire yourself bits of the network, e.g. exclusive use of an elevator, and ride with the drivers if you like. Private is OK and free (no tripods or lighting). https://tfl.gov.uk/info-for/media/filming-and-photography/filming-and-photography-on-tfl
I'm going to ask for it for Christmas. Last year I had a book about the history of the Underground - this will make a nice companion piece.
Well, my copy turned up this afternoon ! I thought I would thumb through it and leave it for later to look through in detail but I couldn't put it down and ended up looking through all 220+ pages.... quite fascinating and I like every photo. Must pick it up again soon and have a second look.......