Technically you can take bike if partly dissamblied, even on the Undergroujd.
Technically I think the rule on British railways is "baggage must fit within a 1m x 1m x 1m space" and that applies at peak hours on trains and all the time on "deep stations" on the underground.
That is what permits folding bikes, and I find the 1m3 rule a lot easier to understand than the "this bike yes, that bike no" stuff.
The actual rule doesn't care what it is that you're carrying... just whether the total of what you're carrying on a train/tube fits within a 1m x 1m x 1m space.
A full-sized bike in bits probably doesn't, and you probably can't move it around easily.
Technically I think the rule on British railways is "baggage must fit within a 1m x 1m x 1m space" and that applies at peak hours on trains and all the time on "deep stations" on the underground.
That is what permits folding bikes, and I find the 1m3 rule a lot easier to understand than the "this bike yes, that bike no" stuff.