Careful, now I think you're both wrong! Though IANAL and it would be good if one of ours would comment. Whisperingwaters's suggestion that there's something to be done on a person-by-person basis is wrong, but also, I think PrettyDamnCosmic exaggerates here:
This is nonsense. There is no requirement for exclusion of the other sex to be proportionate. It's always permissible to have a single sex space just because you want to. Privacy & propriety are the obvious reason to exclude on the basis of sex.
Single sex "space" is not really a concept in the law for obvious reasons, and we usually use the term in a space-time sense - somewhere men are not allowed to be at a particular time, such as a room where a meeting is taking place or a service is being provided. You can indeed have a single sex association just because you want to, but you can't have a single sex service (provided to the public or a section of the public - e.g., not just to members of an association - for payment or not) just because you want to. You have to satisfy this part of the EA:
27
(1)
A person does not contravene section 29, so far as relating to sex discrimination, by providing a service only to persons of one sex if—
(a)
any of the conditions in sub-paragraphs (2) to (7) is satisfied, and
(b)
the limited provision is a proportionate means of achieving a legitimate aim.
(2)
The condition is that only persons of that sex have need of the service.
(3)
The condition is that—
(a)
the service is also provided jointly for persons of both sexes, and
(b)
the service would be insufficiently effective were it only to be provided jointly.
(4)
The condition is that—
(a)
a joint service for persons of both sexes would be less effective, and
(b)
the extent to which the service is required by persons of each sex makes it not reasonably practicable to provide separate services.
(5)
The condition is that the service is provided at a place which is, or is part of—
(a)
a hospital, or
(b)
another establishment for persons requiring special care, supervision or attention.
(6)
The condition is that—
(a)
the service is provided for, or is likely to be used by, two or more persons at the same time, and
(b)
the circumstances are such that a person of one sex might reasonably object to the presence of a person of the opposite sex.
(7)
The condition is that—
(a)
there is likely to be physical contact between a person (A) to whom the service is provided and another person (B), and
(b)
B might reasonably object if A were not of the same sex as B.
(8)
This paragraph applies to a person exercising a public function in relation to the provision of a service as it applies to the person providing the service.