The advent of “the Hox” changed the way London thought of budget lodging: Chintz and linoleum went out, to be replaced by good-looking staff versed in local hotspots and compact rooms that pack in more style and cleverness than the low price should allow. You sleep on a platform bed under exposed brick walls and among set pieces like Union Jack pillows and steamer trunks for chests of drawers. You bathe under a rain shower in a futuristic cylinder. Your continental breakfast is delivered each morning via a bag you hang on the door, which can make you feel like a monkey at the zoo, and there’s free water and milk for your little fridge and an hour of free telephone calls a day, even if you call internationally. Downstairs there’sa grill, a bar, and coffee and free Wi-Fi flowing at all hours, make it as much a gathering place for disaffectedmillennials as it is a way station for travelers. Book as far ahead as possible to keep the price down.