For written English, there is not much difference in British and American English except that the Americans have improvised it whereever they could to look different. Ex. If in British English u hire a Taxi, u hire a cab in USA. I shall give u a few more examples.
British English:( See the difference in the use of tense)Riya is not at home. She has gone shopping.
American English: Riya isn't at home; she went for shopping.
In British English, the correct present perfect tense has been used but the Americans have improvised to their convenience and made it past indefinite tense. Here r some more examples for u to study in vocabulary especially.

British English American English
at the weekend on the weekend
live in X street live on X street
a player in the team a player on the team
Monday to Thursday Monday through Thursday
ten minutes past six ten minutes after six
five minutes to ten five minutes of ten
analyse analyze
cheque check (money)
centre center
colour color
defence defense
dialogue dialog
honour honor
jeweller jeweler
programme programe
metre meter
realise realize
skilful skilfull
theatre theater
traveller traveler
Aeroplane Airplane
angry mad
anywhere anyplace
biscuit cookie/cracker
There r numerous examples with me which distinguish between British English and American Emglish. In accent, the use of the vowel a is made 90% as in ash, bash. In British English there are twenty vowels(speech sounds) but in American English there r only five speech sounds. This is how they have made English more easy, useful and practical. U may post ur specific queries and I shall try to give u the best answer to the best of my ability.