His body lay half-buried in the frozen scree, face-down and spread-eagled in his last agony. Above George Mallory, a couple of thousand feet higher, the summit of Everest stood impassively waiting for other men to try to conquer the highest mountain in the world. For me, also, it was the end of a long quest.

At the age of 12, I met my relative Howard Somervell, a friend of George Mallory's who watched him leave on his last attempt to climb the mountain in June 1924. Somervell told me about his own attempt to climb the mountain without oxygen, and how he nearly suffocated due to a frostbitten larynx. He turned back 1,000 feet from the top.

"We met Mallory at the North Col on his way up. He said to me that he had forgotten his camera, and I lent him mine. 'So if my camera was ever found,'" he said, 'you could prove that Mallory got to the top.'" It was a throwaway remark, which he probably made a hundred times in the course of telling this story, but this time it found its mark.

I spent years trying to prove Mallory had climbed the mountain and became the 15th Briton to climb the mountain, in 1993. In 1999, I organised a BBC-funded expedition to look for Somervell's camera. Instead the searchers found Mallory's body. There was no camera, though, and still no answer to the biggest mystery in mountaineering: who climbed Mount Everest first?

I kept searching for new evidence, and went on eight Everest expeditions searching for Andrew Irvine, Mallory's young companion. In 2006, I tested perfect replicas of Mallory's clothing and deduced that they would have kept him alive on the summit only if the weather remained fine. However, the answer to the puzzle was under my nose the whole time.

Somervell was responsible for the meteorological records on the 1924 expedition, and his work led me to the vital clue. One of the reasons Mount Everest is now becoming easier to climb is modern weather forecasting. Whereas the early British attempts relied on rough dates for the likely advent of the Indian summer monsoon, now the expedition leader has highly accurate satellite photographs and forecasting available by email. The weather window needed for a summit bid can be predicted with reliability.

But there is one variable that is literally invisible: air pressure. If one tries to climb Everest without supplementary oxygen there are some days better than others: high-pressure days, when there are more oxygen molecules in each lungful of breath. Conversely, a day with low barometric pressure may effectively make the summit a few hundred metres higher. A climber nearing the summit without extra oxygen is working at the absolute limit of human capacity, and the difference of a few millibars of atmospheric pressure can make all the difference. Even when you are using oxygen it is merely supplementing the ambient air, so low pressure will affect you, too. A recent study of fatalities on Everest shows that deaths blamed on the weather are usually associated with a big drop in summit barometric pressure. Mallory had oxygen but it had almost certainly run out before he had time to reach the top.

In my reading of the 1924 expedition account I became curious about the unseasonably bad weather throughout the May of that year. The expedition report quotes Darjeeling tea planters as saying that "for at least 20 years, no such weather had been known at this season". Usually the cold winds of winter die down towards the end of April and there is a clear week or so around 17 May. But in 1924, the weather was so appalling between 9 and 11 May that Mallory and Irvine had to abandon Camp III below the North Col, something unheard-of in recent seasons. I wondered whether there was an outside event which might have influenced the weather, and in particular whether El Niño might have been the culprit.

At first glance, a movement of warm water in the tropical Pacific from its usual home off Indonesia across to the coast of South America might not seem likely to have an impact on conditions at the top of Everest. But El Niño, which happens around Christmas every few years, causes atmospheric pressure changes that go hand in hand with the movement of the warm water, an effect known as the Southern Oscillation. It is this that affects global weather; in particular drought in South Africa, increased Eurasian snowfall and a reduced Indian summer monsoon.

This fits the facts: there was a drought in South Africa in 1924 that was recorded as one of the eight worst in the 20th century. And Mallory's expedition report describes how there was increased snowfall in Tibet in May that year and that the monsoon arrived late, enabling Mallory and Irvine to make a late attempt.

The 1924 expedition was remarkable for collecting the earliest data on the meteorology of the Mount Everest region. The air pressure (barometric pressure) was also recorded at Base Camp. Somervell's meteorological data from the 1924 expedition was published in 1926 but it was largely ignored until the Canadian meteorologist Professor Moore analysed the storm that one of Mallory's companions described as "a rather severe blizzard". It probably killed Mallory and Irvine. There was an 18mbar drop in barometric pressure at Base Camp during this storm. This huge drop suggests that the conditions during their summit attempt were much more severe than originally assumed and therefore the appalling weather may well have contributed to their deaths.

Seventy-two years later, another disaster was just about to happen. On the evening of 9 May 1996, a large number of clients and guides were poised to make summit attempts having climbed from the Nepalese Base Camp to the camp on the South Col at 8,000 metres (26,240 feet). There had been high winds all day and the chances of summiting appeared low. The winds died down during the evening, though, and the decision was made to attempt to summit.During the afternoon of 10 May, however, an intense storm with wind speeds estimated to be in excess of 70 miles per hour, heavy snowfall, and falling temperatures, engulfed Mount Everest, trapping more than 20 climbers on its exposed upper slopes. Eight of the climbers died; the highest number to die during a single event near the summit of Mount Everest. The winter of 1995-96 was an El Niño year, too.

Using Somervell's barometric readings, the minimum summit barometric pressure was approximately 331mbar during the 1924 storm. It was the same figure during the 1996 storm. A change in summit barometric pressure of just 4mbar is sufficient to trigger hypoxia (lack of oxygen). Clearly both storms were associated with summit barometric pressures and pressure drops that were sufficient to drive the climbers into a hypoxic state. The pressure drop was larger and occurred more quickly in 1924, suggesting that it may have been even worse than the 1996 "Into Thin Air" storm. In 1924, the summit barometric pressure fell from 341mbar on 6 June to 331mbar on 9 June, a drop of approximately 10mbar. The 1996 storm saw the pressure fall from 337mbar on 7 May to 331 mbar on 12 May, a drop of approximately 6 mbar.

This led me to realise there was an even more seductive and invisible danger at work. Mallory had seen Norton and Somervell get to within 1,000 feet of the top on 4 June using no oxygen equipment. It would seem reasonable to assume that the summit was possible to reach with the apparatus. What he didn't know was that the rapidly falling air pressure was effectively making the mountain higher, and that the incoming blizzard was going to make his clothing very thin indeed.

When I digested these results, I reluctantly had to change an opinion I had held for 30 years. If these figures were true, and if the 1924 blizzard was indeed even worse than that of 1996, then there was no way in which Mallory and Irvine, dressed in their marginal clothing, could have reached the summit of Mount Everest on that fatal day.