I think gender neutral cubicles (supervised, because I totally agree on the ones in Camden!) are the way forward ultimately.
In the meantime, it does put some people in an awkward position. For all the people saying 'you're entitled to use the accessible toilet' it's actually not that simple. A lot of disabled toilets are locked and have pretty tight criteria on who is allowed to use it and yes, often that does come down to having physical disabilities/severe learning disabilities. There is a lot of debate about who should be allowed to use the accessible toilet amongst disabled people and it is awful to have someone have a go at you because 'you shouldn't be in there.' I know that I have had people tell me I shouldn't use the accessible toilet even though I have ASD and can't deal with the hand driers.
As a general rule, no, a 13 year old boy shouldn't be in the ladies toilet. But even outside of SN, there are exceptions, trauma being one of them. If, as an adult woman, I don't feel safe sharing confined spaces with unknown adult men, a 13 year old boy who has been assaulted by men probably doesn't either. If he's only accompanied by his mother and if, for arguments sake, he can't use the accessible toilet, then yes, I think he should be allowed in the ladies. I'm not saying it's a perfect solution, but it's a lesser of two evils. One boy accompanied by his mother is less threatening to the girls and women than adult men are to that boy.
13 year old boys vary a lot in size. Some boys have not reached puberty by that age. One of my DBs was taller than me at 13, the other still passed for a 9 year old.