"Night stand" in American English. "Night table" in British English. Also "bedside table". https://www.google.dk/search?q=night+tables+for+bedroom&hl=da&rlz=1T4ADSA_daDK397DK397&tbm=isch&tbo=u&source=univ&sa=X&ei=ttu7VJXKG8rKOfn7gbAG&ved=0CEYQsAQ&biw=1366&bih=611
Well, whether it's Brit. English or not, I've certainly heard "night table" used in England. It could be because of American influence though. We do tend to pick up the odd word now and then, especially near an American air base, or mutual co-existence such as Brit. and American forces stationed nearby each other, or Brits working in U.S.A coming home with a richer vocabulary, cowboy films, advertisements, etc., etc.