"I park my car in the yard"

What is the origin of the different pronunciation of words like park, yard, cartoon, margarine in American and British English?

In other words, why doesn’t British English generally pronounce the r in such words? Or vice-versa: why does American English generally pronounce the r in the same words?

Broadly, English accents are divided into two categories, rhotic and non-rhotic. All English accents were originally rhotic, and the R sound was typically articulated as an alveolar trill, in contrast with the alveolar approximant of most contemporary dialects. Non-rhotic accents began developing in the Middle English period, and were commonplace by the arrival of modern English, gaining popularity in southern England during the 18th century.

Both the British Isles and the United States, as well as Australia and other areas where English is spoken, have regions of both rhotic and non-rhotic accents. As Alex mentions, notable non-rhotic United States accents include coastal New England, New York, and old-style Deep Southern; the so-called "continental" or trans-Atlantic accent, characteristic of upper-class America through much of the 20th century, was also distinctly non-rhotic. Rhotic British accents are to be found in the West Country, as well as much of Scotland and Ireland.

The difference you're describing is between rhotic and non-rhotic accents. In the UK, rhotic accents have been declining since the 16th century, although they still persist in the West and Southwest.

English was already established in the North American colonies before the decline in rhoticity, which is why it's been preserved in the US and Canada. I think the exception of New England might be down to the fashion in the early 20th century of affecting a Mid-Atlantic (and British-style non-rhotic) accent.

North America was clearly colonised before the start of the decline in rhoticity, whereas Australia, South Africa, and New Zealand were colonised after and therefore have non-rhotic accents.

More detail on wikipedia: http://en.wikipedia.org/wiki/Rhotic_and_non-rhotic_accents

I write as a linguist. There is something called compensatory lengthening in phonology and it's simply that when a sound is deleted, another sound is lengthened to fill up that empty space. This can be likened to sharing a small bed with your partner and then he has to leave for work as early as 3am. you spread out to fill the space he has left and enjoy the rest of your sleep. This is why yard sounds different from bad, cartoon from cat and park from pack. the /r/ has been deleted and the vowel before it lengthens to fill its space. this lengthening is sometimes accompanied by backing and rounding to give /a:/ or /Ʒ/. Your margarine example doesn't quite cut it too because non-rhotic speakers pronounce /r/ before vowels and between vowels (intervocalically) so there s no way you would have pronounced margarine as maj-ah-een. you would not pronounce the first /r/ because it is before a consonant but you will definite pronounce the second /r/ because it is intervocalic(between vowels) so you actually say /ma:ʤrin/ or /ma:ʤrәn/ or /ma:ʤәrin/. You likely say the last one when you are speaking slowly.