Your TSH is at the high end of its range, and your Free T4 of 13.1 is only 11% of its range, which is way too low in the range for many people. In addition you should try to get tested for Free T3, since that is the thyroid hormone that is metabolized by all the cells of your body to produce energy. With those results, it would also be good to get tested for the possibility of having Hashimoto's Thyroiditis. The first test is Thyroid Peroxidase antibodies (TPO ab). If that is negative, then a Thyroglobulin antibodies should follow (TG ab).
A good thyroid doctor will treat a hypothyroid patient clinically, by testing and adjusting Free T4 and Free t3 as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results, and especially not TSH results when taking thyroid med. I expect that since you are in the UK you will have difficulty getting the necessary tests and treatment. The reason being that the NHS dictates that thyroid med should not be prescribed unless the TSH is over 10, or if TSH exceeds the range and FT4 is below its range. By the time that occurs, the patient is usually very symptomatic. To get around this problem, a former UK member described her success as follows:
"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 for your reading and knowledge, I highly recommend reading at least the first two pages of the following link, and more if you want to get into the discussion and scientific evidence for all that is recommended.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
In the paper you will note additional tests that should be done. From you those should of course include Free T3, and Vitamin D. D should be at least 50 ng/mL. Your B12 is lower than optimal so you should supplement with about 1000 mcg daily to raise your level to the upper end of its range. In addition ferritin is very important, and your ferritin is way too low. It should be at least 100. So you need to get a good iron supplement and take about 65-75 mg of iron daily, along with Vitamin C to prevent any stomach distress from the iron.
But your main hurdle will be getting a doctor to agree to prescribe thyroid medication. The more you know and become a strong advocate for you own health, the better the chances are that you will get a doctor to treat you clinically, as described. If that becomes impossible, could you go private?