The headline left me with a touch of cognitive dissonance, since in AmE carts tend to be small, relatively powerless things--like the cart that a donkey might pull or a go-cart. And dust, well, is dust. It wouldn't need a large vehicle, would it? But, of course, a (BrE) dustcart (which is staffed by dustmen) is what Americans would call a garbage truck (staffed by garbage men--though, of course, in both countries I'm sure that their official job titles are suitably euphemistic). In the BBC News article, they also refer to the vehicle as a refuse lorry (=AmE truck--kind of...but that's another post for another time).
Reversing dustcart 'caused death'
So, it left me thinking of other kinds of carts. Like (AmE) shopping carts, which in BrE are shopping trolleys. Which made me think of other trolleys, like (BrE) tea trolleys or serving trolleys, which in AmE would be tea carts or serving carts. Which made me think of the announcement one hears at the (BrE) railway station/(orig. AmE) train station: "A trolley service of soft drinks and light refreshments will be available on this train." One usually has to go to the café car on an American train to buy refreshments, but if they did come around with refreshments-on-wheels, it would not be called a trolley service. In fact, the only AmE use of trolley that I can think of is one that the OED marks as AmE: "an electric car driven by means of a trolley", the latter trolley being a kind of pulley system. In the US these might also be called (as in San Francisco) cable cars. [See comments for correction of my understanding of the pulley system involved!] In the UK, such things are generally called trams--a term which no longer implies the use of a pulley system. The trams found in the UK would be called streetcars in many dialects of AmE. The OED marks an AmE sense of tramway, referring to the cables on which suspended cars travel--but I can't claim any first-hand knowledge of that sense.
Photos from image-searching dustcart and tea trolley. For a past post on (BrE) rubbish/(AmE) garbage collection, see this one.