Fears for the 33-year-old former SAS officer from Oxfordshire grew after his solo ascent took him through a third night without oxygen above 23,000 feet. After 48 hours the risk of altitude sickness, and even brain damage, increases.
He became the first climber to make a successful ascent of the 29,000ft peak without oxygen, from the Nepalese side. But appalling weather and snow blindness forced him to delay his descent and face a fourth night on the mountain.
Earlier, Mr Taylor and the expedition leader, John Barry, tried to reach a more sheltered camp lower down. They were forced to turn back and decided to sit the storm out in Camp Four, hacked into the ice face 3,000ft below the summit.
'Harry's actually taking oxygen now,' an expedition spokeswoman said last night. 'It will not affect his record, because he got up and down without it. They are in a very dangerous position up there, but there's nothing they can do about it at the moment.'
A fellow climber, Rebecca Stephens, from London, descended to Camp Three yesterday and was said to be returning to the shelter of Camp Two with two Sherpas. Her attempt to become the first British woman to scale Everest will be postponed until the weekend, organisers of the DHL Everest 40 expedition said.
The expedition was launched to commemorate the 40th anniversary of the first ascent by Sir Edmund Hillary and Sherpa Tenzing in 1953.
Members of the DHL party also hoped to join the search for the nephew of Sherpa Tenzing, who has gone missing with another expedition.