Have you tried Stella O’Malley? She’s in Ireland but you could have video sessions if you can’t find anyone local.
I expect Stella is pretty full but IME the handful of therapists/counsellors/psychologists/psychiatrists who are public about following an explorative model rather than an affirmation model have behind the scenes networks of fellow professionals who are also explorative/trans skeptical but more low key about it.
My daughter has video sessions with one of the psychologists who left GIDS and went public about her concerns, but DD is very cagey with her having read up on various mental health disorders and ‘conversion therapy’.
Please do what you can to stay away from Gender GP. The founder is current suspended by the GMC and her husband has been permanently struck off. The company is technically run via some weird shell-company type overseas arrangement. Even extremely pro trans people have criticisms about their lack of adequate follow up, especially for females taking testosterone who need a regular full blood count test due to risk of polycythemia.
www.endocrinologynetwork.com/view/transgender-men-receiving-testosterone-at-greater-risk-of-blood-clots
Unfortunately GenderGP will prescribe to your daughter without your permission as long as she can pay their fees (and have done so for much younger children).
If your family is low income or your daughter can somehow demonstrate financial estrangement from you, GenderGP have a fund that covers their own fees and the costs of prescription drugs for a year, so they will literally provide a controlled substance to teenagers for free without parental permission for 12 months (and then they expect the minor to start paying if they want to continue).
all of this is documented online, lots of it on their own website (except the critique of inadequate follow up care, obvs).
lots of UK pharmacies have started to refuse to fill GenderGP private prescriptions for minors but they do seem to have a Romanian doctor on the payroll who puts her name to the paperwork, so Irish pharmacies might just accept it due to EU stuff? Might be worth looking around for a trans Ireland message board to lurk on?