I'm from north London, I've got a Londonish accent, I do pronounce my H, cannot stand that southern Plaaarstic elaaarstic, I even heard someone on the radio say Chaaartum when she meant Chatam Kent, talk about chalk squeaking across the blackboard, oh yes, and a Lancaaarster Bomber, orrible.
I have a relative that drops his H almost all of the time, except for when he refers to an arris rail on a wooden fence, which in fact doesn't have an H, I daren't catch my wife's eye when he says it.
Regards ippy