It was the craze that delighted bargain hunters yet horrified environmentalists: British tourists flocking in their thousands to New York and other US cities to pick up designer clothes and electronic gadgets for half the price back home.

Yet amid the pound’s longest run of losses against the dollar for 37 years, the travel industry fears belt-tightening Britons’ predilection for US trips will wane – and with it their near-£15bn ($28bn) annual contribution to the American economy – if sterling continues to slide.