I see. But even if they don't allow you to leave the station can they force you to complete the journey you have paid for? Do BTP have the authority to physically manhandle you onto a train going to the destination that your ticket indicates?
No, neither. The only authority a member of gateline staff has to physically interact with the passenger is to detain them if they refuse to provide their name and address, or to remove them from the railway using reasonable force under the common law rights of the land's occupier or owner (as the case may be), or under the Railway Byelaws for being reasonably suspected of committing an offence thereunder.
None of the relevant railway offences are indictable offences and hence no 'citizen's arrest' is permissible: only a police office etc. may arrest for a non-indictable offence (*
opens can of worms exceptions*).
If a passenger breaks their journey on a ticket which does not permit this, the passenger is liable to pay the excess (difference) between the fare paid and the cost of the cheapest ticket permitting break of journey for their journey. If they refuse to pay, they must give their name and address such that the matter can be followed up later. But if they offer to pay, or to give their name and address, I see no power for them to be detained (at least by a member of railway staff).