Puberty blockers are prescribed off-licence.
Indeed, but the licenses are for specific drugs. So if they promote Lupron or whatever specifically, they're definitely in trouble, but would the rule prevent promoting "puberty blockers" in general? Even if NO "puberty blocker" is licensed?
Reading through the docs on your link, I don't find it clear. You definitely can't name any treatments:
Unlicensed medicines should not be mentioned, to comply with regulation 279 of the Regulations which prohibits advertising of medicines for which no marketing authorisation or registration is in force. Treatments that involve the use of unlicensed medicines may not be described as ‘clinically proven’ or similar.
That seems to make it clear that you would be in trouble making claims about the benefits of puberty blockers, if they're all unlicensed.
But I can't see anything in there directly ruling out people providing a prescription service for off label drugs in that document, as GenderGP do, as long as they don't name them, and are careful about the claims made. They would of course have to answer to their own regulators about whether the prescriptions were suitable.
This is the general guidance:
On the homepage, only indicative prices for a particular medical condition may be provided, for example, “Erectile dysfunction treatment - £20 for a medical consultation, £50 for an initial course of 4 treatments.”
And then there's more blurb about how you could provide price lists for specific treatments, but that wouldn't apply for off-license stuff as per the previous quote.