djbaggysmalls some MPs are listening. (Some MPs never listen whatever the topic is). The soft spot at the moment is the medical intervention with children.
I also think Woodpigeon is correct in that as a private member's bill it is unlikely to become law, especially given the legislative workload of Brexit & the 2 year deadline to complete that in once article 50 has been triggered.
That said, in many public services, it seems to be that practice already seems to recognise self declaration. There does need to be Parliamentary scrutiny of safeguards which the equalities committee has failed to do, as they have ignored red flags from a number of (non-feminist) experts such as the British Psychological Society.
Medical intervention with children (under 18) also needs better scrutiny. Waiting increases the risk of several children having unwanted side effects from Lupron, as have already emerged in the US from children who were prescribed this for growth issues. We don't yet know what the psycho-social effects are of postponing puberty are. Cross sex hormone treatment from the age of 16 has irreversible effects,especially for girls taking testosterone. We could wait until we have a generation of de-transitioners , or we could put in better safeguards now.