I thought I would come back and update you on my experience and it is valuable for other people to know. I have finally, this week, managed to persuade a Dr that the cough, which I have still had all this time, (six months) was due to the Levothyroxine and she gave me a new prescription. I took it to the chemist and specifically asked for a different brand, which they got for me. I have been taking the new brand for four days now and the cough has practically disappeared. If this happens to you, whilst you need to go through all the tests to make sure that the cough is nothing more sinister, don't let the Drs tell you it isn't possible, because it is.