Well, I am interested in this too. It seems an unresolved question. Iodine deficiency is a major cause of hypo. Up till recently it was thought that iodine deficiency was not a factor in the UK, but that was just because no one had tested to see if we were deficient. (Hah! Typical.) Two studies now have found fairly widespread iodine deficiency, one in young girls, one in pregnant women. No study to my knowledge has yet bothered to test UK hypos at diagnosis for iodine status. My guess is that it will turn out to be widespread amongst us.
The main researcher in the UK on this is Martin van der pump of the Royal Free. If anyone inherits a fortune in the next few months, please pass him some so he can carry out this study. If you search his name and hypothyroidism and iodine in Pubmed his studies come up.
Iodine is of course essential for thyroid function.
Now the complex part. Some research has suggested that giving iodine in Hashimoto's can make it worse - "like pouring petrol on a bonfire" or something like that. I have looked at some of the research, but there is no firm conclusion to be drawn. Does it raise antibodies? In some studies, not others. In areas where there is iodine deficiency giving iodine supplements sometimes results in cases of Hashi's suddenly being identified - is that because it is causing it? Or is it unmasking it? That is, is it possible that giving iodine to someone starved of iodine with antibodies raises the TSH - but they already had all the symptoms? We don't know, because researchers rarely ask participants the "unscientific" question, "How do you feel, what are your symptoms?"
Could this even be the answer to the mystery of low TSH with obvious hypo symptoms - iodine deficiency? That's a wild surmise of mine, but you couldn't rule it out I think on the research as it stands.
Some doctors suggest that giving iodine is OK so long as you have selenium as well, that it is having the two minerals out of balance that is the problem. I think that's probably a surmise rather than proven too.
Meanwhile, back in the real world as patients, I think it is worth thinking about diet. The main source of iodine in the UK is milk. Fish is also a good source. I know I would have probably been iodine deficient from the age of about five, in that case.
Those with unidentified intolerances to casein and lactose, and celiacs - I wonder how much iodine they absorb, however much milk they drink?
Maybe we should all club together and crowdfund Vanderpump.