I've just been diagnosed with Hashimoto's and prescribed Levothyroxine. It's standard practice to retest after 8 weeks but I didn't want to start taking it if my GP surgery couldn't book me in for a follow up blood test due to Covid-19. When I called they told me they're no longer doing routine blood tests; however, when I said I'd just started taking thyroxine (I'd previously said medication) it was like saying the magic words!
I imagine many GP surgeries are following similar guidelines so you might find it helpful to mention that you're taking Levothyroxine if you need to book a follow-up blood test. 🍀