As others have alluded to, if you are taking Thyroxine you need to have regular blood tests (TFTs) to ensure your dosage levels are correct. This is a standard procedure and it’d be questionable if your GP wasn’t having them carried out.
As for the hospital not carrying out these tests, with it being a community prescribed med often the prescriber (your GP) has to order the routine blood tests and, due to the way various financial incentives work (not sure if TFTs attract QOF points, I work in secondary care not primary) its likely the GP will want to keep them in house. This said though, when I have needed bloods taken I’ve just got my GP to print off the order form and had a colleague do them at work. It may be that you can ask for similar from your GP and kill two birds with one stone when you’re next at the hospital.
As also alluded to, I would recommend booking an appointment with your GP if you feel your medication intake needs reviewing. GPs are notorious for polypharmacy-ing patients and one of the roles junior doctors have within secondary admissions is wading through patient medications and reducing them to manageable levels (both for our benefit and more importantly, the patient’s). This is not an outright criticism of GPs, the nature of their workload means that often they have very limited time to deal with issues such as this.
Finally, if you’re not happy with your GP service tell them or complain to your local Clinical Commissioning Group. Nice Dr Smith the GP is a private contractor billing their services to the NHS. If no one complains then said GPs continue doing what they’re doing, billing the NHS for sub-par service with the NHS ‘proper’ (secondary care/hospitals) picking up the pieces.
It’s your NHS.