"Does the legislation (any/all of it) recognise a difference between males / females and TIMs and TIFs though?"
The law allows you to separate things by sex where it is reasonable to do so. So for instance, separating girls and boys in order to subjugate the girls at a co-ed Islamic school recently was found not to be reasonable, whereas separating men's and women's toilets is not only reasonable but specifically required in workplaces that have non-private bathrooms.
In general the law refers to 'sex', however most sex-based distinctions will be discretionary, so it's not necessarily the case that you CAN'T have men in a women's prison.
In the case of a provider that WANTS to provide different (or no) facilities based on biological sex then that is legal IF that is a proportionate aim. Obviously the interpretation of 'proportionate' is tricky.
If it's NOT deemed proportionate, then it will be gender reassignment discrimination.
And if the person has a GRC, then you can't exclude them at all, they are legally of the acquired sex.
Separate sex changing rooms very specifically are proportionate.
data.parliament.uk/writtenevidence/committeeevidence.svc/evidencedocument/women-and-equalities-committee/transgender-equality/oral/24014.pdf
"The Act allows trans people to be excluded from single-sex
services in some situations. How certain are you that those provisions are used proportionately, appropriately and fairly?
Nicky Morgan: I suspect overall they probably are. I am not sure that we have necessarily evidence. There are certainly examples. I have some here:
female victims of sexual assault; public changing rooms; bathing facilities and toilets, which I know is a huge area; and certain procedures in hospitals where it would be appropriate to have single and separate sex services. We should be very clear this is not a green light for discrimination. There is a line between discrimination and legitimately offering single-sex services. We are aware of only one case, which relates to a pub in Halifax, which was heard at Halifax Crown Court last year. "
www.lawcentres.org.uk/policy/news/news/kirklees-law-centre-wins-landmark-transgender-discrimination-case
The transperson had lived as a women for 20 years and had had GRS (although it's never clear what GRS actually means).
It was a very low level non-binding case in a County Court and it was not clear if the pub had adequate legal representation, nor whether the case was decided on going to the wrong toilet (possibly justified) or being banned from the pub (not justified)