I thought we had established that!
So a refusal to allow people to merely cross, rather than travel, may be acceptable and legal, however inconvenient.
It would depend on what was agreed between the relevant parties at the time of the public funding of the footbridge extension referred to by a previous post. I suspect nothing was set out because, at that time, no one thought it an issue! Manual ticket barriers had been done away with at Sheffield (and many other stations) with no thought that they would ever return - manual or otherwise. I know they existed at Sheffield because I got caught by them, in the 1980's. Trying to travel on a West Yorkshire Day Ticket into Sheffield to then buy a South Yorkshire Day Ticket - I wasn't trying to avoid the fare, merely trying to avoid alighting at the boundary station to buy one. Had to buy a single from the boundary to Sheffield and then buy my day ticket at the ticket office!