I was being slow on the uptake because I had forgotten, or never knew, that Newnham is still single-sex.
They're only exempt from sex-discrimination law in this case because there's a pre-1990 instrument (the 1917 College Charter) requiring them to appoint women as fellows. Their announcement refers to Article 3 (attached) which is about promoting women's education generally, but the College Statutes presumably contain more by way of detail.
Schedule 22 para 3 is about employment. I don't know why single-sex colleges are allowed under the Act, but they clearly are. AI thinks it's a Schedule 3 matter, and might very well be right, but there could (also) be a relevant 'enactment' under Schedule 22 para 1 for all I know (the Act contains its own provisions for single-sex schools).
Whatever. If the college is to get out from under its sex equality obligations under the Act, it has to obey its Charter and any relevant laws and - if it's relying on Schedule 3 - admit only biological females as undergraduates.
Why am I banging on about this? Because it's just one example of the way in which civil society (insofar as it embodies different or separate treatment of the two sexes) is held together by a Heath-Robinson arrangement of laws, instruments, and custom. This plays into TRA's hands by making the application of the SC ruling beyond a tight reading of EA2010 itself tricky, if institutions can't be persuaded to do the right thing. And it seems quite a few of them can't.