@Vinculum Oh no, not the National Portrait Gallery too! There definitely used to be female-only toilets on the lower ground floor, but that was before the renovation - I haven't been down there since. Thanks for mentioning the female-only toilets on the 4th floor, but it's typical that they'd be tucked away and most people wouldn't know about them.
On a more general topic of women's toilets design (when we are lucky enough to have them) I'm often surprised at how poorly designed they are. For example, in theatres, they need to allow for a very high throughput during the intervals. And that depends on the people queuing being able to see when a cubicle becomes free.
I used to go to the Proms at the Royal Albert Hall a lot. There are largish Ladies toilets on the ground floor, and although there was always a long queue along the corridor in the intervals, the queue used to move fairly quickly. But in 2019, after they'd been renovated, the queue was moving significantly more slowly. And it was all due to a simple change - the cubicle doors are now self-closing. Previously, once someone left the cubicle, the door would stay open, but now they close themselves within a couple of seconds.
The layout of the toilets is awkward. If you're at the head of the queue, you have to keep looking to your right to spot when someone has exited one of a row of cubicles. And you also have to look straight ahead to see if anyone has exited one of the cubicles on the far side. If you're looking ahead when someone comes out of a cubicle on the right and you don't notice it, when you look back, you used to notice that the cubicle was now empty because the door would be open. But now, the cubicle door shuts within a couple of seconds - by the time you look back to the right, the cubicle door is shut, the woman is at the wash basins, and you can't see the free/engaged indicator on the door. So you don't know the cubicle is now empty.
So what continually happens is that cubicles stay empty and unused for several minutes because no-one noticed the women coming out of them. So the queue is much slower-moving. I've often noticed a cubicle on the right coming free, and as I walk towards it I check the other doors and see a couple of them are empty, but no-one has noticed.
I also remember the Ladies toilets at the Bridge Theatre in London when it opened several years ago. The problem there was that there were a lot of cubicles around the room, but in the middle was a double-sided row of washhand-basins, with mirrors above them. It meant that if you were at the head of the queue by the door, you couldn't see if someone exited one of the cubicles on the far side, because of the mirrors getting in the way. So again, cubicles would often stay empty because no-one had noticed as the women left them.
Small design issues, but they can have big impact on the efficiency of use of toilets in a theatre. Did the designers not think of this?
If toilets are now being converted to mixed sex, with enclosed cubicles containing wash basins, that makes things worse because you spend longer in the cubicle washing your hands. In a busy place like a theatre, that will slow things down.
On the original topic, I've been to many performances at the Old Vic over the years, but I won't go now, simply because of the lack of women's toilets.