In terms of the Byelaws, there is Byelaw 13. If the member of staff has reasonable belief that this is being breached, they can remove the person using reasonable force under Byelaw 24. Even if a judge later found that the person was not, in fact, loitering - there only has to be reasonable belief on the part of the member of staff. That's a much lower bar than you are suggesting.
Under common law, every person who owns or has possession of a piece of land (in this case, Network Rail own and possess Euston station) can ask someone who is there by virtue of the 'implied right of access' to leave. If the person fails to do so, they become a trespasser and so 'self-help' - i.e. reasonable force - can be used to remove them.
There are
many trespass offences specific to the railway. In this situation,
section 16 of the Railway Regulation Act 1840 makes it an offence to wilfully trespass - again, this is triggered when the person is asked to leave and fails to do so. S16 also gives railway staff - and anyone else they call to assist them (so even potentially a member of the public) - the power to detain such trespassers until the police arrive.