I've known it with a silent "h", so "an honest man" as opposed to "a helpful man".
The silent "h" occurs in some words of French origin:
but not in others.
whereas a hard "h" will occur in words of Germanic origin
In terms of accents:
The French, when speaking English, will often drop the "h"s since it is not pronounced in French, e.g. Les Halles is pronounced "lay al". On the other hand, I have been asked in Paris by an American "Do you know where Les Halles (les hal-les) is? Had to think for a moment what they meant.
In BrE, an East London, South London, or Cockney accent also drops "h"s, because, well, that's what they do. So they may say "elpful" for helpful.