From the BBC web site here:
http://www.bbc.co.uk/news/magazine-11642588
Quote
British English dictionaries give aytch as the standard pronunciation for the letter H. However, the pronunciation haytch is also attested as a legitimate variant. We also do not ask broadcasters who naturally say haytch to change their pronunciation but if a broadcaster contacted to ask us, we would tell them that aytch is regarded as the standard pronunciation in British English, people can feel very strongly about this and this pronunciation is less likely to attract audience complaints.
Haytch is a standard pronunciation in Irish English and is increasingly being used by native English-speaking people all across the country, irrespective of geographical provenance or social standing. Polls have shown that the uptake of haytch by younger native speakers is on the rise. Schoolchildren repeatedly being told not to drop Hs may cause them to hyper-correct and insert them where they don't exist.
Jo Kim
BBC Pronunciation Unit