In Britain, a street-food selling place can be referred to as a kiosk or booth but generally it is only if it is in the name of the company who owns it. Most of the time, I have only heard the term van.
Van is most often used in Britain, as in kebab van
or burger van.
The thing with burger vans and kebab vans is that they generally don't just sell burgers. Whilst the name refers to their primary product, they sell other cooked foods.
Kebab vans sell burgers too and both kebab vans and burger vans provide hotdogs, bacon, sausage or egg baps in any combination such as egg and bacon, along with hot and cold soft-drinks.
You may have ice-cream stalls where the stall is static,
but travelling ice-cream stalls (which sell house-to-house for example) would be ice-cream vans.
You also have travelling sandwich vans selling sandwiches and cold soft-drinks workplace to workplace.