DD
You can indeed claim back tax on MM. Be careful though as not all military "duty" travel qualifies ie IIRC you cannot claim for a 1771 "duty" journey to attend a medical appointment, again IIRC, only for journeys where you had to travel as part of your day job ie to attend a meeting at another unit etc. IR do a good booklet on what is and isn't eligible an a quick call to your tax office will see one dispatched to you (unfortunately I cannot remember the IR number though it may be on the IR website).
You can back date the claims for previous years but I think there is a limit to how many years. You might need some form of proof for the atxman that you did the journeys, and although the old SAMA print out was not acceptable as proof it was a very useful document for totalling the mileage you had done and what rate you were paid.
Interestingly every year I have filled in the full and short tax return the IR have ended up owing me money.
This year I haven't received a tax return of any sort - should I be worried? Shadwell, over to you!