Yes, it's one of these quaint usages. It used to refer to the Ministry of Transport, which I am not even sure exists anymore (at least under that name). It was then applied to the MoT Test, the car inspection for roadworthiness, which then became elided to the form of "the MOT" being universally understood to refer to the test itself, or even the certificate you gain for the vehicle passing the test. From a vast body of civil servants to a piece of paper!