It has always been pronounced "haypenny" over here, so far as I'm aware, although quite often with the initial "h" dropped. Which makes some sense of the following tale:-

In London Zoo, a new monkey was born, much to the delight of the whole troupe in the enclosure, and to the keepers who tended and cared for them. Unfortunately, this little primate was deformed, having been born without any knees.

The keepers were most distressed about this, fearing that the little fellow would die, until the youngest and newest keeper, a youngster just out of school, had a brilliant idea.
"'Ere," he said to the Head Keeper, "I know what we could do to 'elp the por li'l bleeder!" (London zoo keepers tend to speak in this sort of language, and the swear-word at the end is accepted as a term of endearment in this context!)
"Wot's that, then, son?" asked the Head Keeper.
"Gi's a penny, then," the youngster said, "An' I'll nip rahnd the shop an' get 'em to change it for two 'ayp'nnies."