My housemate (very definitely an English girl) has
Haidee as har middle name (named after a great aunt, I think).
She pronounces it hay-dee, and I think that's the most likely pronounciation for English speakers.
Heidi <
Adelheid has no connection to
Haidee.
Haidee appears in a poem by
Byron (I think it's
Byron :) ) and thus had some vogue in Britain during and after
Byron's (?) lifetime.