Sir Ranulph, who lives near Exford, was trying to raise £3 million for the Marie Curie cancer charity from his feat.
Now, he has vowed not to try to climb Everest again.
He had hoped to reach the 29,000 feet summit at 03.30 BST on Saturday, but the 64-year-old had to turn back after contending with heart problems and vertigo.
Sir Ranulph suffered a heart attack during his first unsuccessful attempt to scale the mountain three years ago.
He had set off from base camp on Tuesday and was accompanied by guide Kenton Cool and medic Robert Casserley.
They reached the final stopping-off point in the ascent after negotiating the ‘death zone’.
However, they had not had enough rest as the team had to set out on the final stage of the ascent in the dark because of impending bad weather.
Despite being only a few hundred yards from the summit, they were forced to turn back to base camp after resting
Sir Ranulph said: “I am not exhausted, I just had not had enough sleep.
“You have to accept these things. I am not crying over spilt milk but it was agonisingly close to the summit.
“Luck is not with me on Everest. I was within an ace of doing it. The following day I got back down to base camp in one go. I have got punch if I have had a chance to recharge my batteries.”
His wife, Louise Fiennes, told the BBC that he was keen to return to the UK immediately.
She said: “He just called me an hour ago and asked me to arrange to get him back to Kathmandu. He is desperate to get back to the UK.”
Iswari Paudel, who owns the company which organised Sir Ranulph’s climb, told the BBC he would be flown out by helicopter on Sunday morning.
Sir Ranulph was making his second attempt on the peak despite suffering from vertigo and heart problems and currently being in remission from prostate cancer.
He was the first man to reach both the North Pole and the South Pole by land, ran seven marathons in seven continents in seven days shortly after heart surgery, and journeyed to discover a lost city in Arabia described as ‘the Atlantis of the Sands’.
- Our photograph shows Sir Ranulph on Everest. Photo by Kenton Cool.