When I had my extra weight, it was ALL around my middle. It took me almost a year, but the 30 some odd pounds did eventually come off. My trick was to cut out sugar, drink lots of water and increased my fiber. I was on myfitnesspal and watched my calories and carbs closely. What worked for me may not work for you, but I thought you would like to know that it can be done. Oh, and this happened before medication. I finally got ins right before I got the last 5 pounds of the weight off and that was when I was diagnosed.
From noticing that you are in the UK, I expect that you are being medicated with T4 only, and just med enough to get your TSH within range. Is that correct? If tested beyond TSH, please post your test results and their reference ranges shown on the lab report. Also, if tested for Vitamin D, B12 and ferritin, plese post those, with ranges, as well.
How much T4 med are you taking, and what other symptoms are you having?