I think that what the Labour party actually said was that they thought that no adjustments to the Act were necessary? But if anyone can prove they have said something categorical that recognises that it IS necessary to amend the Act I would really like to see it.
At the moment it is impossible to exclude any male with a GRC from female single sex spaces because they are 'legal women' - there are some very limited exceptions to this, therefore were service providers to attempt to prevent legal women from entering women's single sex spaces they would be able to claim discrimination under the Act (as currently drafted by the previous Labour Government) because they have the benefit of the protected characteristic of both sex and gender reassignment. This is a consequence of the Haldane judgement. Add to that no male can be asked for a copy of the GRC so it's de-facto self ID.
So where Labour talks about spaces for biological women, if they intend that to mean biological women excluding the these legal women they need to amend the Act.
You would think, in the light of all of the women who are asking for this clarification they would just clarify it (if it is indeed the intention of Labour to make these amendments).
I presume they are currently doing some significant fence sitting trying to appease both the TRAs and women. Neither should be satisfied with what they are currently saying because it's not at all clear.