Uber Technologies Inc. faces a severe threat to its business in London as the U.K. capital’s authority for transport matters plans a wholesale overhaul of the rules governing the private car hire trade, including an English-language requirement for drivers and a mandatory five-minute wait time between ordering a ride and pickup.

The proposed rules, contained in documents reviewed by The Wall Street Journal, set out what Transport for London calls a new vision for the future of the taxi and the private hire trade as a whole.