The Fowlers thing has reminded me.
A lot of words beginning in h come from the french, where it is very rarely (if at all?) pronounced. French used to be the language of court in England, so those words are “most correctly” pronounced following the french pronunciation of a silent h, and consequently preceded by an an.
Interestingly, the french may have at one stage pronounced their hs. Look at “hôtel”. the circumflex over the o replaces an s which once followed it (made it easier to write, took up less space cheaper on paper or something(?) so hôtel used to be hostel, which we also use in English, a word which must have into English usage before “hôtel” and from which I think no-one, no matter how toffee-nosed, would drop the h and recede with an an.