LONDON—Global demand for crude oil could peak in the next two decades, as renewables like solar power surge faster than expected to meet a greater share of the world’s energy needs, BP PLC said Tuesday.

The world’s appetite for oil and other liquid fuels could continue to grow until around 2035, hitting 110.3 million barrels a day—compared with 95 million barrels a day in 2015—before plateauing and falling off in the run up to 2040, the British oil-and-gas giant said Tuesday in the main future scenario, releasing its annual...