But only where it is a proportionate response to a legit need. If there are adequately private changing facilities (and apparently these are going to be upgraded to ensure they meet the relevant standards), surely there is no legal requirement for single-sex swimming to be provided.
The legal challenge would need to come from non-trans-identified men (in the ladies pond) and non-trans-identified women (in the men's pond). And even then, for the challenge to succeed, they would have to prove some sort of detriment, presumably? Which would be hard if the men's and ladies ponds offered similar benefits to one another - and even harder because of the existence of an everyone-welcome mixed-sex pond.
Also, regarding the names of the ponds, the Equality Act doesn't directly state rules about the naming of facilities as such. It just holds that calling a service single-sex when it isn't in fact single sex (bcs there are transwomen using it) is legally null in the sense that it doesn't do anything to establish that the provider is making needful provisions for women.
Possibly consumer laws might entail restrictions on the name?? -- at any rate they would require the pond providers to make it absolutely clear that the ladies pond wasn't single sex.
Although personally i feel really sad that the women's pond can't be left alone by men, I'm starting to feel that if it is genuinely true that a majority of users prefer the trans-inclusive arrangements, these arrangements should be allowed to stand,