I asked my GP to request that I be tested for Free T3 and Free T4 as well as TSH, as advised by the endocrinologist. The nurse who took my blood wrote this on the form, but she said sometimes the lab does not do the requested tests, they just do the ones they want to. So it came back and they had just tested T4 and T3 and TSH.
I had blood tests at private hospital when I saw the endocrinologist privately and they charged me £157 for the phlebotomy and three blood tests. Looks like I will have to pay this again if I want to see what is actually going on with my blood levels. Grr.