Yes, it doesn't have to be a medical process. A male who put on a dress and declared unequivocally 'I am a woman' would I think be covered.
However, where a person identifies as non-binary, gender fluid, moon gender or whatever, it's not clear they are reassigning their sex at all because those are not sexes. From the trans equality report:
95. Our evidence also called into question the extent to which the Act protects people with broader kinds of trans identities, who may not be seeking, or may not have sought, gender reassignment, medical or otherwise. We obtained a legal opinion on this point from expert barrister Claire McCann, who told us that people falling within such a broader definition of trans identity could have “no certainty” of being protected from discrimination.
96. Ms McCann explained that when the Equality Bill was going through Parliament the then Solicitor General had clearly indicated that it was only the provision in respect of discrimination by perception which would protect those members of “the wider transgender community” who did not come under the protected characteristic of gender reassignment. That is, they would only be protected if they were discriminated against because they were perceived to be proposing to undergo, to be undergoing or to have undergone gender reassignment. The difficulty with this provision is that there are likely to be cases where an individual from the wider trans community, is discriminated against because of who they are and not because they are perceived to be transsexual. Mr Morton gave us an example: “if they have come out as non-binary, they are being perceived as non-binary, not as transsexual”.
publications.parliament.uk/pa/cm201516/cmselect/cmwomeq/390/39007.htm#_idTextAnchor245