Some examples:
Aluminium. Over here we say 'al-u-min-i-um'. You say 'aloom-i-num'. Neither nation can spell the word.... (Aluminiumiumium?)
Beer. What you call beer, we call lager. What we call beer, you call disgusting. This might be mutual.
Cookies. You eat these with milk and with great self control you only eat two at a time (you don't? naughty!). We call them biscuits. You call biscuits those dry crackery things that might go in soup (or at least in the part of the US I went to).
Flummoxed? Our US chums will be if you use this word. It means to be confused. The typical reaction of the average Brit upon arriving in the US. Then again you might be 'hit for six' (i.e. upset to the point of falling over) by it all. Which just isn't cricket, eh chaps?
Hard. In the UK, you might see an unshaven tattooed uncouth man with big muscles in a pub. If you accidentally spill his beer, he might get upset and request you to join him outside. He might say `Come on then if you think you're hard enough!' Or even 'I'm hard, me, so you better watch your step, mate.' He is not casting aspersions on your sexual persuasion, nor does he have an erection. He is merely stating the fact that unless you buy him another pint of lager in the very immediate future he might beat seven shades of shit out of you. In the US, our friend the male actor would probably say 'I'm hard' while sharing a bottle of woody flavoured chardonnay with his co-star...
Kip. In the UK to have a sleep or a nap. A kip house is apparently a brothel. Being young and innocent I was unaware of this...
Randy. In the US a perfectly reasonable first name. Pity then, the multitude of poor Americans given this unfortunate appellation when they come over to old Blighty. Wherever they go, grimy street urchins snigger, little old ladies try desperately to stifle guffaws and ordinarily quite sensible members of society burst out in laughter. And why? In the UK, saying 'Hi, I'm Randy!' is akin to saying to our American cousins 'Hello friend, I'm feeling horny.' However, save your pity for poor soul Randy Highman who introduced himself to my supervisor at a conference not so long ago...
Roundabout. Imagine you are travelling in the UK along the M3 into Basingstoke (why I can't imagine - it's a God forsaken place.) You have already worked out that a motorway is the same as a freeway and you are feeling pretty pleased with yourself. In front of you is the biggest rotary you have ever seen. In the UK, we call them roundabouts. To instill a morbid fear of these things in our children we force them to play on minature versions of them in playgrounds (wooden disk that turns around with bars to hold onto) and make them watch endless re-runs of the Magic Roundabout*. This program was originally a French satire on politics in the late 1960s though it looks just like a animated kiddies show made by someone on SERIOUS acid. Sugar cube eating dogs indeed. *
Stuffed. To be full up after eating too many cookies. Also 'Get Stuffed' a cookery program for insomniac students and people on a low income, where you are told how to make fancy versions of beans on toast using everyday ingredients like baked beans, bread, butter and curry powder. The recipies are invariably called things like 'Currybeanytoasty-yum-yum-a-go-go'. As well, 'get stuffed' is something you say to someone who isn't your best mate.
Toilets. Although we have a lot of colourful euphenisms for the lavatory experience in the UK (e.g. spend a penny, watering the daisies) we lack the prissiness of our American chums. To us a toilet is a bog, a kharzi, a shithouse (or alternatively an outhouse in more polite company), a gents/ladies but mostly a toilet. It is perfectly acceptable to be in the Ritz and request to use the toilet. However, you guys seem ashamed of the t-word. Hence you go to the John (where no-one called John is there) and the bathroom (where there is no bath). ...And a word of warning for English chaps in the US - never admit to eating baked beans out of the can.
Link:
http://www.dur.ac.uk/~dgl3djb/~ukus.html
* About The Magic Roundabout:
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https://en.wikipedia.org/wiki/The_Magic_Roundabout
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https://en.wikipedia.org/wiki/Le_Man%C3%A8ge_enchant%C3%A9