Yes, most dialects of British English drop the R but this is replaced by vowel lenghtening. Thus wod and word are different because the vowel is lengthened in place of the lost R. It is a mistake to say the r is just pronounced different. Look at any International Phonetic Alphabet transcription in a British English dictionary and you'll find the r is not there. This is the difference between rhotic and non-rhotic. RP (Received Pronunciation), the "posh English accent" is non-rhotic. Thus car is really something like /ka:/ with a lengthened vowel. However, there is still a "linking r". Thus when you say "a car and a book" in a non-rhotic dialect, it is pronounced "a ca: rand a book". The r sort of attaches to the next word.

However, traditionally, English is rhotic. Non-rhoticity (r-dropping) has been spreading from the southeast of England and has gradually taken over most of the country. The American pronunciation of English is more conservative and archaic.

BTW, Shakespeare would have originally sounded more American than English. So movies like "Shakespeare in Love" are really historically inaccurate. No one had posh English accents in those days because they hadn't yet developed. The vast majority of England even in the 19th century pronounced R like Americans do. The West Country dialect of the South of England still retains this pronunciation.

Nicholas