I just saw your post and didn't want you to be left hanging with no replies as that must have taken a lot to share.
This is such a tricky journey. There are a lot of online support groups, both for young people who are unsure of how they identify and for the parents wanting to support them through it. These communities are experienced, empathetic and kind. All characteristics that (a) your family needs and (b) your mother seems unwilling to provide.
You could start with Wandsworth THRIVE's LGBT Forum
https://thrive.wandsworth. gov. uk/kb5/wandsworth/fsd/service.page?id=An1xRld0D0A
Families Together supports families of LGBT children
https://www.familiestogetherlondon . com/
Or this list of Wandsworth based services should be helpful
http://wandsworth . lgbt/wandsworth-lgbtq-services/
My advice, FWIW, is to focus your energy on finding the support that is out there, rather than throwing energy away on someone who doesn't seem interested. I'm not on the same path as you but have had to seek out communities where parental support was lacking, so I appreciate the ache and disappointment that you must be feeling.
Wishing you the best.