A reminder that toilets in the UK are NOT single-sex spaces whatever Falkner wants you to believe.
Many of us have been caught desperately short in a long queue at the Women's in a nightclub and run into the entirely empty Men's. It's accepted practice. That would be illegal if they were single-sex spaces.
Taking your child of a different sex into the loos to wee in a cubicle because you can't send a toddler in alone, illegal.
You get the picture.
Putting the Gents and Ladies signs up is a suggestion for the purposes of societal norms. It doesn't create a single-sex space for the purposes of the Equality Act. It *could* potentially, but it overwhelmingly doesn't. This is what Sumption was saying, though he hinted he thought that could change.
If Falkner has her way, it will. Enjoy wetting yourselves when you're out clubbing ladies, and don't try to take your male baby into the Ladies anywhere lest you suffer the wrath of the Gender Police