I just tell my GP (specifics via DM if you want) that I need to test [insert hormones here] (eg estradiol, testosterone, progesterone) for unrelated to the purpose of the appointment reasons in addition to testing for low vitamin D or whatever, and they give me a link to book, for free, on the NHS
This GP is pretty good at not asking questions and just doing what you ask for (within limits, they refuse to give a bringing prescription)