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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.
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not the deeper lines e.g picadilly and whatever the other colours are called. I found this out recently.
Hammersmith & City and a few others, yes.
Here's something more informative: http://www.squarewheels.org.uk/bike/LUbikes
I wonder if S&S get around the "no full size bikes on this peak hour train service" type deal?
I remember having to help a US woman in Majorca put her S&S bike together. She could manage the frame but the cable joiners were too hard for her. She needed Di2 brakes :)