The addition of the letter ‘h' to the front of ‘aitch'...ie the name of the letter itself...is generally regarded as uneducated, though it definitely IS becoming more common in day-to-day usage. In fact, The Oxford English Dictionary - the ‘bible' of English words - does not even list it.
It seems to have originated in Irish English and is relatively common in Australian speech. It may be that - like the rising intonation at sentence ends - Australian soap operas have had some influence. That is possibly because many Irish religious Brothers took teaching positions in the early days of settlement there.
I cannot confirm what follows, but I have been informed that, to this day, one can tell whether someone is an Irish Protestant or a Catholic by asking him to recite the alphabet, The latter, it is claimed, invariably says haitch.
As long ago as the 1700s, the addition or omission of an opening ‘h' was common in British regional speech, giving rise to forms such as the two following...
(a) "If a haitch and a ho and a har and a hess and a he don't spell 'orse, then my name haint 'enry, awkins."
(b) "Rifle butts are made of hoak, hash or ‘ickory." So said the apocryphal army drill-instructor.