They are relying on Schedule 12. The relevant explanatory note reads as follows:
877.This paragraph allows a single-sex institution to refuse to admit members of the opposite sex. An institution is defined as single-sex if it admits students of one sex only. An institution which exceptionally admits students of the opposite sex, or which admits a comparatively small number of opposite-sex students to particular courses or classes only, is still regarded as single-sex. Limiting those students to particular courses or classes is permitted. However, other forms of sex discrimination by the institution against its opposite-sex students would still be unlawful.
Examples
- A women’s college which admits only female students is not discriminating unlawfully against men.
- If the college admits a small number of men to make up the numbers on a particular course of study, it is still regarded as a single-sex college. It is not discriminating unlawfully by refusing to admit men to other courses.
- A women’s college which admits men to certain courses but refuses to let them use the student cafeteria would be discriminating unlawfully against them.
(emboldening added by me)
This Schedule appears to be a carry-over from the SDA, intended to enable eg mixed-sex sixth forms and catering for students of disciplines favoured by the opposite sex (Steve goes to catering college/Debbie does motor mechanics). (It was a different world! Everything was supposed to go co-ed eventually. )
The qualification for a male to attend Newnham, then, is that it is being done "exceptionally", with no further explanation. I can see why their lawyers seized on it.