I don't know a whole lot about British pronunciation, but my impression was that h-dropping (i.e., failing to pronounce the h at the beginning of a word) is considered "low class", and is not present in RP (Received Pronunciation, "the Queen's English"). It is also my understanding that RP is the standard dialect used in broadcasting, public speaking, etc., or at least it was until recently (I seem to remember John Wells blogging about Estuary English overtaking RP in public settings in the past 10-20 years). However, I noticed in a news clip from the 70's or 80's that the newscaster failed to pronounce his h's. There was one particular example that caught my ear. The clip was about Gary Glitter, a pop star from a few decades ago, who was arrested. The newscaster said, "Gary Glitter 'as been arrested." In rapid speech I probably wouldn't even have noticed the h-dropping (after all, even in American English we would probably drop the h in that situation), except that in the newscaster's non-rhotic dialect the "r" at the end of "Glitter" jumped out at me. Since he pronounced the "r", I had to surmise it was in onset position, which means there couldn't have been an h.
So I guess my question is for any British English speakers, or anyone else who knows: what's the deal with h-dropping? Is it common among broadcast speech?