It could well be linked to the additional Public Sector Equality Duty on local authorities, as private clubs obviously don’t have that obligation.
And I think the community the pool serves makes a difference too in terms of discharging the PSED - council pools in some areas might not need to bother, whereas my public pool has sex-segregated sessions as there’s a high proportion of Muslim and Jewish swimmers who wouldn’t be able to swim otherwise.
I think for Hampstead, it would be difficult for an organisation that’s been running separate women’s, men’s and mixed facilities for years and years (albeit incorrectly in recent years, due to Stonewall’s shoddy advice) to argue that everything should now be mixed and that women-only and men-only spaces are suddenly no longer needed.