"I'd rather not put chemicals in my body"
This one is held sincerely and it's worth being fair to it. Nobody wants to take something they don't need. A tablet a day for the rest of your life is a large thing to accept, and accepting it feels like conceding something about your body that you'd rather not concede. The wish to be someone who doesn't need medicine is a wish for health, and there's nothing wrong with it.
Two things, though. The first is that the condition is a chemical too. High cholesterol is a substance in your blood. An underactive thyroid is a shortage of a hormone. Depression, whatever else it is, is happening in a body. The choice was never between chemicals and no chemicals. It's between the ones your body has arrived at on its own and one more, chosen by someone who's seen what the others do.
The second is that this belief is a good reason to have the conversation and a poor reason to have the quiet stop. If you'd rather not take a statin, that's a legitimate thing to say to a GP, and the NHS statins page itself lists other medicines for people who can't or won't take one. If you'd rather try to bring your blood pressure down by other means first, prescribers hear that every day, and the NHS page on high blood pressure puts lifestyle changes before tablets. What you can't do from the drawer is find out whether your case is one where that's safe. The quiet stop takes a real preference and turns it into an unmonitored experiment on the one body you've got.
So keep the preference. Say it out loud, to the person who can act on it. The reader who says "I'd rather not, what are my options" gets options. The reader who stops and says nothing gets a repeat prescription in the post and a check-up they're avoiding.