Long long ago in a land far far away called Newcastle, I remember my primary three English teacher telling me that Americans had lazy English and that the British pronunciation was the original. She told me about the words herb and island.
audio 1
So let's look at a word with two pronunciations. A herb is a (noun) plant used to flavour food or used as medicine. (In botany, a herb is a non-woody annual plant.) The American pronunciation is usually 
without the h, while the British pronunciation is usually 
with the h. (British pronunciation is also sometimes without the r. British English only started lazily dropping the r in words during the late 18th century and the early 19th century. However that is another topic.)
Normally it is difficult to decide how a word was pronounced centuries ago before sound recordings. However, we can sometimes get clues from poetry. In this case we get an answer from articles (the, a, an). We can show this pronunciation by looking at whether older writers used "an herb" or "a herb". In this case, my example is from a famous cookbook.
Take twelve Gallons of water, a handful of Muscovy (which is an herb, that smelleth like Musk), a handful of Sweet-Marjoram, and as much of Sweet-bryar.
audio 2
So the word herb was originally pronounced without the h in England. The modern American pronunciation is the original. The 17th and 18th century British people who went to America took their pronunciation with them. Sometimes it was the British who changed and the Americans who kept the original pronunciation.
The pronunciation actually makes much more sense, because herb was originally spelled erbe in the 12th century. It was borrowed from the Old French word of the same spelling. The h was added three hundred years later, probably to make it look more like the Latin word herba. The h was only pronounced as recently as the 19th century.
audio 3
So what my old English teacher taught was wrong! I also remember her telling us that the word island was originally 'correctly' pronounced 
in England and 
in America. According to the Oxford University Press Dictionary she was wrong again. Both countries use the same pronunciation, . In addition to some naive ideas about language, she was making the spelling-pronunciation error. In Old English the original spelling of island had no silent s. It was added in the 15th century, at about the same time as herb got its h and for the same reason. Sometimes English spelling does not match the way we say a word. It is clumsy on both sides of the Atlantic, but that is English.
audio 4
by John Larrysson
A native English speaker who has been teaching practical English in Hong Kong for more than a decade.