I don't understand why specific conversion therapy bans are desirable to anyone anyway.
For the healthcare side of things (including legitimate psychotherapy), there are existing safeguards from professional standards, medical ethics, practice guidelines etc. that prevent the use of futile and/or harmful treatments. Actual gay conversion therapy from genuine registered therapists is in practice nonexistent in the UK.
I do think we need better regulation of the whole talking therapy field, with better transparency and protection for clients and patients. But the best and most responsive protection against useless and dangerous treatments would come from research and regulation from within the field, with recourse to the usual types of legal redress in case of harm, not slow national implementation of legislation against specific therapies and treatments.
Anything outside of that system isn't "therapy", really, and most would either come under abuse of some kind (including religious abuse), or should be covered by freedom of belief — if somebody had for example a religious belief that being gay was wrong, and freely sought out religious counsel or advice (not therapy from a licensed or professionally registered practitioner) from a cleric who believed likewise, surely that's allowed? I don't think I'd want to ban people from having opinions I disagree with and discussing them with others who share those opinions as part of a broader framework.
We do need better protections against all kinds of harmful and coercive acts, including bad healthcare and religious abuse. But I think a specific conversion therapy ban might be a tacit admission of failure to properly regulate psychological and psychotherapeutic aspects of healthcare and protect those who seek such care, and failure to protect vulnerable members of society or act on abuse of vulnerable people in the community.