This is interesting as last time I spoke to DVLA, the woman told me that the exemption no longer exists! But from posts here it plainly does.
Another thing to watch is that (I work in law) I used to often see exempt vehicles getting fixed penalty notices for failing to display excise licence - invariably they would say that they were exempt - but they were exempt from *paying*, not from displaying one, as of course it was used as a way of ensuring you had MOT & insurance each year - so although they got them for free (I presuming this is still the same?) some thought it meant they did not even have to apply for one - which in those days meant it cost them £30 to find out they were wrong the hard way!