I had mine done this week. My blood was taken in a tent in the surgery car park by a nurse in full PPE. Call from the Diabetes Dr the next day to discuss results (which were good). Slightly concerned by the speed of response, but Dr said she had a spare slot so she called me rather than leaving...
Just because you can't drive, doesn't mean you can't go and buy another parking ticket. I doubt a parking company would quibble if you at least tried to pay for the extra parking.
Having said that, it would seem worth writing to the parking company and explaining what happened.