Recently we have seen that people are still getting short prescriptions for levothyroxine - typically one month. This inevitably results in problems for patients when there are supply issues. In my book, levothyroxine should normally be prescribed for a minimum of two months on each prescription – and you should be able to keep at least a month ahead of the game. That is, you should be able to request your next prescription while you still have about a month’s supply in hand. Then you can ring round pharmacists, ask questions here, submit your prescription to an on-line pharmacy, … That is, do whatever you need to do if there are any supply problems.
When first started on levothyroxine and there are likely to be regular dose adjustments, it might be reasonable for a GP to keep prescribing periods shorter. Once on simple repeats without any alterations, there is no reason to keep to short periods. Why even the MHRA agree! On page 21 of the MHRA’s levothyroxine report  from early 2013, it says as recommendation number nine:
Levothyroxine should be prescribed and dispensed in quantities covering three months supply, where appropriate, in order to address issues of continuity of supply and also to improve convenience to patients.
Please do whatever is necessary to avoid having short period prescriptions. In the first place, simply ask. Then maybe print off a bit of the MHRA’s report if you need to support your argument? Note that the report justifies its recommendation on two separate grounds: continuity and convenience.
I get a two month prescription but I have plenty in hand and it is relatively easy for me to get to the GP surgery, and to visit numerous pharmacies if required. So I won’t bother going through the process of asking for a change for me.
Obviously, if you obtain any medicines by other means, the argument that you need to keep plenty in hand applies even more strongly.
 MHRA publishes a report on levothyroxine tablet products: A review of the clinical and quality considerations