I wanted to ask why in the world the doctor didn't just do the necessary testing and find out instead of speculating that it "might be" an autoimmune disease. Even with the restrictions of the NHS in the UK, the doctor should have been testing beyond TSH and then treating you with thyroid hormone medication. Sounds like he is lost and just postponing any decision about your status.
To determine if you have the most common cause for high TSH and hypothyroidism, Hashimoto's Thyroiditis, the doctor should run two tests. Thyroid Peroxidase antibodies, and Thyroglobulin antibodies, usually listed as TPO ab and TG ab. In addition, TSH is a pituitary hormone that is affected by so many things that at best it is only an indicator to be considered along with more important indicators such as symptoms and also levels of the biologically active thyroid hormones, Free T4 and Free T3. Note that these are not the same as Total T4 and Total t3, so you should insist on testing the Frees, not Totals.
Also, since hypo patients are so frequently low in the ranges for Vitamin D, B12 and ferriitn, those should be tested as well, and supplemented as needed. D should be about 55-60. B12 in the very upper end of its rnage, and ferritin should be 70 minimum.
I know how difficult it can be in the UK to get adequately tested and treated. One of our UK members who was finally successful told us this.
"What I have learned from my experience is that you have to go to the Dr's office and TELL THEM WHAT YOU WANT and to go backed up with knowledge. You have to tell them that you have done your reading and looked into your condition and care about the long-term treatment of your health and thyroid. If you fight for what you want, you will eventually find someone that is happy to go along with your wishes. But we all have to take charge of our own health, right?"
So keep in mind that a good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and free T3 as necessary to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just TSH levels. You can get some good insight from this link written by a good thyroid doctor. Use it with your doctor to try and get the needed tests and treatment. If you are unsuccessful with your doctor, try other doctors. The other alternative might be to go private.