I take my bike onto trains and they are allowed into carriages. They use the space that is for wheelchairs and should, as once happened to myself an three others cyclist three wheelchairs got on at a station so we were all moved around in the carriages. I don't think they are anymore of of a h&s risk than some of the buggies, especially twin buggies, that are carried on the trains. You should moan at the train operatives to put on more carriages not the people who use them.
Army horses loose on London streets