According to this article written after the Piddock interview Labour intend to change the Equality Act from saying ‘gender assignment’ to ‘gender identity’.
Not sure how Sex as an exemption then works or could work.
A Labour spokesperson said: “Our commitment to reforming the Gender Recognition Act to introduce self-declaration for transgender people is undimmed.
“Labour will amend the Equality Act 2010 to ensure it protects trans people by changing the protected characteristic of ‘gender assignment’ to ‘gender identity’ and removing other outdated language such as ‘transsexual’.
“The Equality Act will continue to allow for separate and single-sex services, providing that such treatment by a provider is justified, but no spaces will be permitted to discriminate against trans people.”
Shadow cabinet minister Laura Pidcock told Today: "I think that there has to be the enforcement of single space exemptions for women to heal and recover and it is absolutely crucial that there are spaces, that there is provision, for trans people to also get the help and support they need."
www.independent.co.uk/news/uk/politics/labour-manifesto-trans-rights-women-only-spaces-single-sex-corbyn-a9214656.html