I'm not sure they can be "single gender" though.
If you look at the judgment, when referring to single sex associations, it points to Schedule 16 of the Equality Act, which says that an association can restrict membership to persons who share a protected characteristic.
But gender isn't a protected characteristic.
Sex is, which means you can restrict membership of your association to members of one sex and exclude the other. (This goes both ways, but it is important to note that it will be much harder to justify the existence of a single sex association for men only, because it will be harder to meet the criteria in the Equality Act showing that it is reasonable for men to object to the presence of women.)
Gender reassignment is, which means you can restrict membership of your association to trans people and exclude everyone else. (This only goes one way, so you can't restrict membership of your organisation to people of either sex who are not trans, and exclude trans people, because being cisgender not being transgender is not a protected characteristic.)
Similarly, you can restrict membership of your association to LGB people and exclude heterosexuals. Technically you could restrict membership of your association to heterosexuals and exclude LGB people, because being heterosexual is a sexual orientation and therefore a protected characteristic as defined in the Equality Act, but again, I think you would struggle to justify why straight people have a legitimate need to associate without gay or bisexual people.
But the Equality Act does not appear to allow associations to restrict membership to people having a characteristic which is not a protected characteristic, which gender is not.
I am trying to think of an example of where membership of an association is genuinely restricted to people having non protected characteristics and I am struggling a bit. Lots of associations have rules about membership based on other characteristics such as ability to pay a membership fee (discriminates against poor people), ability to pass an audition (discriminates against people who can't sing in tune or play a musical instrument), ability to be safe in the water (discriminates against people who can't swim), to give a few examples, but none of these would directly and lawfully discriminate against gay/female/trans/black/old people. (There may be indirect discrimination.)