However, if I see a trans person in the female bathrooms, i have no idea whether they have fulfilled the conditions or not and (in some ways rightly) no right to ask. As the cases discussed on this thread and others suggest, there are people who are being allowed into female spaces on their own say so, and this is accepted*
The current law does protect people from discrimination once they have undergone the process of gender reassignment. The equality act change has been around since 2010:
From the Act
Gender reassignment
(1)A person has the protected characteristic of gender reassignment if the person is proposing to undergo, is undergoing or has undergone a process (or part of a process) for the purpose of reassigning the person's sex by changing physiological or other attributes of sex.
(2)A reference to a transsexual person is a reference to a person who has the protected characteristic of gender reassignment.
(3)In relation to the protected characteristic of gender reassignment—
(a)a reference to a person who has a particular protected characteristic is a reference to a transsexual person;
(b)a reference to persons who share a protected characteristic is a reference to transsexual persons
I am not sure how this protected characteristic relates to someone who just says they are trans - and what evidence is needed.
I think that the proposed changes in law relate to getting a gender recognition certificate and demedicalising that.
There has been leglisation for the last 7 years making gender reassignment a protected characteristic.