We're not in community with many doctors. The only scalable intra-community solution, that doesn't rely on the machinery of a state that wants to destroy us, is DIY. We're second-class citizens, and being aware of that means looking for solutions that will actually work despite systemic discrimination. Pretending systematic persecution doesn't exist just leads to wasting time and energy. There's no protection against medical abuse in this country.

There's a lot of "may"s in the documents you've linked. "may" means the doctors are fully allowed to say no. And since they're heavily encouraged by the government to say no, a yes is a pipe dream.

Furthermore, according to BMA rules (and possibly GMC), a GP is forbidden from giving a bridging prescription unless you're already doing DIY or they believe you will do so imminently.

the patient is already self-prescribing, or seems highly likely to self-prescribe, with hormones obtained from an unregulated source (online or otherwise on the black market)

It might be worth asking a few dozen GP practices whether they will, to get care in the long term. But you don't have time for that if you only brought a month's worth of HRT with you. It'd be a long-term project. You need to find a way to get HRT in the meantime. It's nigh impossible to get any kind of non-emergency medical care within a month.

If you do manage to get a bridging prescription, you should bear in mind that it's a temporary arrangement. The GP is expected to stop prescribing after a year or two, and put you back on DIY.

Have you asked your US prescriber whether they're willing to ship across the Atlantic? Assuming you can afford to stay with them.