Mount Everest. We learn about it when we are very young in New Zealand. Our own man, Ed Hillary, conquered it, the tallest mountain on Earth, we write in our primary school projects. We might add that Tenzing Norgay was with him.

Although the late Sir Edmund emphasised he was part of a large expedition - led and driven by the British - he came from a small country that has relished the individual glory he achieved from such a world-beating feat of exploration.

The cultural myth surrounding Hillary - the centrality of this towering figure to our concept of ourselves as a nation - has, understandably, fed the notion of New Zealand as a country that "punches above its weight".

So it is not surprising the idea two Britons, Mallory and Irvine, may have beaten Hillary and Tenzing to the top by 29 years, finds less resonance here than in Britain.

This enduring mountaineering mystery resurfaced this again a month after the Australian adventurer Duncan Chessell, a member of the New Zealand Mountain Guiding Association, announced he would hunt in the frozen, oxygen-starved "death zone" near the top of Everest for the remains of Andrew "Sandy" Irvine.

The high altitude detective work has become an obsession, almost an industry, for climbers from Australia, Britain, the United States and Germany. And the tragic tale of Britain's local fellows Mallory and Irvine, seems more appealing to Britons than the story of Hillary's triumphs in Asia and Antarctica.

Chessell reached the 8848m summit of Everest with his commercial expedition this week, his third time on top of the world and a record for an Australian. He diverted from the last section of the descent to the top camp to spend 90 minutes searching for the body of Andrew "Sandy" Irvine and the camera which could solve the 86-year mystery, if it contains recoverable images shot from the summit in 1924.

British expeditions tried for decades to claim the prize of Everest. George Leigh Mallory became climbing leader of the third British expedition, in 1924. It tackled the mountain from the Tibetan side, up the North and the North-East Ridges. Hillary's successful expedition in 1953, led by Sir John Hunt, approached from Nepal and up the South-East Ridge.

On June 8, 1924, Mallory, a strong climber, and Irvine climbed well up the North-East Ridge to within several hundred metres of the summit - and possibly much closer.

They were sighted from lower down the mountain by their colleague Noel Odell around 1pm ascending one of the rock steps - cliffs - that form the main climbing obstacles on the ridge. The sighting came through gaps in the gathering clouds of a snow storm that engulfed Everest that afternoon.

The Second Step, the most difficult, now has a ladder fixed to it and there is controversy over whether Odell saw them there, on the First Step, in which case it is unlikely they reached the summit, or on the Third.

Another theory is that they may have traversed under the Second Step and ascended the Great Couloir (a wide gully), the route which Everest expedition veteran and researcher Graham Hoyland - a relative of 1924 expedition member Howard Somervell who climbed high on the mountain - maintains was the favoured route at the time.

"I read all the pre-war expedition books and I realised no-one had even attempted to go anywhere near the Second Step. They'd all traversed underneath it," Hoyland told the Guardian in 2007, before claiming in a presentation to the Royal Geographical Society that Mallory and Irvine were the first on top.

Theories diverge, too, on their descent and deaths. Some argue Irvine gave his last oxygen bottle to Mallory before giving him a "shoulder-stand" up the Second Step, waiting for him to return, then eventually heading down alone, losing his way and perishing from the extreme cold and shortage of oxygen. No-one can survive for long in the death zone, above 8000m.

On this theory, Mallory reached the summit by late afternoon or early evening, descended the Great Couloir in the dark, but dropped down too far before turning right and aiming for the North-East Ridge. He fell or was perhaps hit in the head by a falling rock - and died.

Chessell believes Mallory made it to the top alone, helped up the Second Step by Irvine, and that on their descent together, they had an accident while roped together on the First Step.

Speaking to the Weekend Herald from the 6500m Advanced Base Camp on Thursday, after an overnight rest on the descent, Chessell says, "I think Mallory has been lowering Irvine down the First Step and Irvine slipped and this caused the rope to come tight on him and probably pulled Mallory off his stance. Irvine dropped down the rock at the bottom of the step. He might be a long way down - enough to pull Mallory off. Mallory falls full length of the First Step, the rope catches on rock and breaks, then Mallory crashed down the face."

Guided by the research of climber Jochen Hemmleb, Conrad Anker found Mallory's body in 1999 at 8160m, around 300m below where Irvine's ice axe was found in 1933.

The 1924 team's cameras were not found and are assumed to lie with Irvine; nor was the photo of Mallory's wife found. Some believe he intended to place it on the summit, although others theorise the picture and a camera may have been removed from Mallory decades later by a Chinese climber who revealed having found the body, but who died the next day in an avalanche. After being found again in 1999, Mallory's body was buried in a scree slope on site.

Other artefacts linked to the pair have been found: a felted wool mitten turned up in 2001 and a spent oxygen cylinder, both on the crest of the North-East Ridge between the First Step and the "exit crack", the point where climbers from the north now usually join or leave the ridge.

Chessell, and Hemmleb's German-Austrian team, both searched for Irvine this week, apparently without success, in an area of caves and rock clefts called the Warts, which is about 50m along the ridge beyond exit crack.

Chessell said in the lead up to the search that it was the best chance in years of finding Irvine because high winds had scoured snow off the area and might have exposed the body. But on his eight-strong team's summit day - the day of the search - there had been an unexpected dump of snow, and with strong winds, "They were the worst conditions I have ever encountered by a factor of at least 10 on the summit."

It was a harrowing day. On the ascent, his team found a Japanese climber who had died after summiting the night before. And another climber, from a US team, "died on descent and we were not able to help him on our descent".

He took time out from his descent to search for Irvine, but with 1.5m of hard-packed, wind-blown snow, there was no hope. Afterwards adding a mystical touch, Chessell comments: "... I couldn't help thinking that the mountain was acting to keep its mystery to itself. The snow was unbelievable and came from nowhere."

Irvine, thought to be in the area called the Yellow Band, has probably been found before.

Says Australian writer Ben Sandilands: "He was stumbled across on the Yellow Band by Chinese climbers in 1960 and 1975 and by an exhausted solo climber in 2003, who had strayed off the usual route and was lucky to reach a lower camp and assistance in getting off the mountain alive."

He says Chessell was the only "openly declared" entrant in this year's apparent "race" to find Irvine.

Hemmleb, who has written books on the mystery, was described by a mountaineering website as an "Everest detective" leading a German-Austrian climbing team that also planned to look for Irvine during this May's summit season.

Chessell said Hemmleb's team spent about two hours looking.

A leading New Zealand mountaineer, Graeme Dingle, is not surprised Irvine's body has not been found.

"Irvine probably went down the North Face. He's probably down on the Rongbuk Glacier."

"Frankly I think Irvine's body will be buried under many metres of snow and ice and one day it will emerge at the end of the Rongbuk Glacier. But it will be a long time before that happens."

He dismisses the idea that Mallory and Irvine reached the summit.

"There's virtually no chance they could have done it," he says - a view echoed by Hillary's son, Peter, who has twice reached the summit, via the South Col.

"There's an extraordinary amount of evidence to say that really, it isn't likely that they reached the top," says Peter Hillary.

What effect do these men think it would have on New Zealanders and the memory of Sir Ed if it was convincingly shown Mallory and Irvine got to the top first?

For Peter Hillary, the question can't be answered because the matter is "totally circumstantial at the moment".

Dingle is more certain. "I don't think it would make much difference. Ed was esteemed for many things. You might have a debate about who was the real messiah; that debate goes on anyway."

Sir Ed himself said in the 1980s that proof of Mallory's getting there first would have downgraded his and Tenzing's achievement, although he suggested that to claim "a complete first ascent", climbers must descend safely too. "I'm rather inclined to think, personally, that maybe it's quite important, the getting down."

Peter Hillary laments the attention given to the Mallory-Irvine mystery. "I think it's a shame we are perhaps not hearing more of the stories of who is doing the most dynamic climbs on the mountain."

Duncan Chessell is already scheming about his next search for Irvine, again fitted alongside a commercial expedition taking clients to the summit, but with a larger search team.

While mystery remains, someone will investigate.