The Trusts need to have clear no bullshit no hand waving no Oooo be kind policy no using the word "should".
The Board of the Trust have a leagal obligation to follow the law and to protect the assets of the organisation by not engaging in actions which will lead to preventable litigation.
Just as the employee is sackable for stealing or any other gross misconduct the onus is on the Board to approve the clear and easy to understand policy.
In this case they can even write the process of investigation who, when, where, why, witness, proven to be true etc
Starting point is clear policy
Males can and may only use male open changing rooms and male block toilet or any other MSSS.
Females can and may only use female open changing rooms female block toilets or any other WSSS
[(Edit) Or obviously a single unit. ]
And any instance it staff objecting must be reported to HR (either directly or by the manager it is reported to) and the investigation may only be managed by HR.
And put it in as a one liner in the Board meeting pack if need be.
Any person proven to be using the provision for the other sex is engaged in Gross Misconduct the person will be given one final warning. The second time it happens the person will be sacked for cause.
The employee can try take them to court but if its a HR led process done professionally (they may need new hires) and follow the policy and is be preparing on the basis its going to the ET the Trust should have a watertight case. So the Judge cant rule on breach of process nor a breach of law.
This ^ also allows staff to as another employee to directly say "stay out" before it has to becomes a matter for investigation so the individual has a choice and a second chance.
Draconian?
Authoritarian?
Yes
So what !
Adults need to be able to follow the law and work rules before being let loose on the general public.