At 7.41am British time yesterday she radioed news of her achievement to expedition organisers, with the jubilant message: 'I'm on top of the world.'
Ms Stephens, 31, reached the summit (29,028ft, 8,848m) with two Sherpas by racing up the final 3,000ft (914m) in a 'window' between two vicious weather fronts.
The expedition leader, Peter Earl, said from their base camp that the party had reached the summit 'in the nick of time'. He said there were no problems on the ascent, although there had been a delay at the top because the climbers had not realised where they were. 'She is a very, very happy girl,' he said.
Her physical condition was good: 'She's in great shape, no frostbite, nothing,' he said, adding: 'She's as tough as old nails.'
Ms Stephens is the 17th woman to reach the summit. The first was Junko Tabei, of Japan, who made the ascent in 1975 when she was 36.
Ms Stephens, a travel and property journalist from west London, set off for the summit on Sunday morning with her former boyfriend, John Barry, and three Sherpas. But Mr Barry and one Sherpa had to turn back suffering from fatigue and altitude sickness.
The expedition marked the 40th anniversary of the first ascent of Everest by Tensing Norgay and Edmund Hillary, and it took the same route, via the Western Cwm and South Col. It is now the most popular way up - known by cynics in the trade as the 'Yak route'.
Ms Stephens, who worked until two months ago for an expatriate magazine published by the Financial Times, is a relatively inexperienced climber; she describes herself as an 'amateur'. She took up climbing in 1989 after reporting from Everest on an Anglo-American attempt on the mountain's north- east ridge.
'Since then,' she wrote in March, 'I have become quietly obsessed . . . The addiction takes a hold, like any drug. And now I want to be the first British woman to reach the top of Everest.'
She has spent her holidays on the addiction: last year she climbed Alaska's Mount McKinley, the highest mountain in North America (20,320ft, 6,194m) in conditions that killed several other climbers.
Faith Glasgow, a colleague of Ms Stephens at Resident Abroad magazine, said yesterday: 'She's very determined, very resourceful and good company. She falls on her feet - always. You just watch with your mouth hanging open.'
Mountaineers praised Ms Stephens. Julie-Ann Clyma, who yesterday announced plans for an ascent without oxygen on K2, the world's second-highest mountain, said: 'Rebecca Stephens's achievement is incredible, particularly because I understand she has only been climbing for a few years. It's a real demonstration of her conviction to have got there.'
John Major congratulated her on a 'magnificent achievement'.
What's so heroic? Page 18
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