Wikipedia has a page on List of British English Words Not Used in American English to help people understand the different terminology between these two very similar languages.
Also check out American and British English differences, list of American English words not used in British English, list of words having different meanings in British and American English, and for phrases in Britain that have no equivalent in America see Britishisms.
Here are some examples of British words not used in America:
agony aunt – advice columnist
argie – Argentine
answerphone – answering machine
anti-clockwise – counter-clockwise (counter-clockwise is sometimes used in Britain)
approved school – school for juvenile delinquents; reform school
balls-up – error, mistake, snafu (this is commonly misinterpreted as referring to the testicles, however, it is in fact an old horseman’s term referring to when the hooves get packed with snow)
bang to rights – dead to rights
the dog’s bollocks – the bee’s knees (something excellent or top quality)
dole – welfare, specifically unemployment benefit
dosh – money
gobsmacked – utterly astonished, openmouthed
to go pear-shaped – to go West; i.e, for a process to suddenly go wrong
gogglebox – television set
googled – confused (from a cricketing term for a type of delivery bowled, the googly; predates Google.)
gormless – lacking in intelligence; with a vacant expression
green fingers – green thumb
randy – (also horny) horny
wally – buffoon, fool; milder form of idiot. Now considered an old-fashioned word.
wank, wanker – to masturbate; one who masturbates, timewaster, now generic insult
wee – verb and noun for urine and urination (also wee-wee); Scottish, Irish, and northern English for small