A storm is expected to hit the mountain today and Miss Stephens cannot afford any delay on the 3,000ft climb from Camp 4, where she rested yesterday.
'There is a window of opportunity and she has decided to go for it,' said Doug West, spokesman for the DHL Everest 40 expedition, which is commemorating the first ascent of the mountain in 1953.
Miss Stephens, 31, a journalist from London, suffered a setback when her fellow-climber, John Barry, was too exhausted to accompany her on the final leg of the climb. Three Sherpas accompanied Miss Stephens.
Snowstorms had forced her to postpone the climb from Camp 4, at 26,000 feet, but she finally set off at 6pm Greenwich Mean Time last night. She estimated that it would take her 12 hours to get to the summit and six hours to get back down.
Harry Taylor, 33, who last Sunday became the first Briton to climb Everest from the Nepalese side without oxygen, arrived back in Britain yesterday with frostbite, exhaustion and snow blindness.