A few points
Trans women are legally permitted to use women's bathrooms in Britain.
Are you sure you "can always tell"? There have been cases of cisgendered women in bathrooms being wrongly targeted by gender critical women.
Back to Linehan, what is he doing inside women's toilets again? Does he keep glancing inside women's toilets to look for trans women? What about the stalls, does he check over the tops of them too on the lookout for trans women? Is he the national appointed women's toilet monitor?
I also bet we've all passed a trans women at some point (in or out a bathroom) without ever knowing it. There are people on twitter "transinvestigating" photos of people trying to determine their biological sex and still not being certain, so how can you tell for certain just briefly passing someone?