Henry Bowers, Apsley Cherry-Garrard and Bill Wilson took 35 days to collect three emperor penguin eggs in July 1911. In the middle of the Antarctic winter, they had to survive intense blizzards and temperatures that plunged to –60C. It was pitch black and the three had to navigate by candlelight and the stars. They took turns falling into crevasses. Cherry's teeth chattered so violently that they shattered, while Wilson was blinded in one eye by a blob of boiling blubber from a camp stove.

In the end, the three men – members of Robert Scott's doomed expedition to the south pole – returned to their base camp, utterly exhausted and close to death, with the three penguin eggs packed in their sleds. Cherry never recovered from the ordeal – which he vividly described in his book, The Worst Journey in the World – while Wilson and Bowers died with Scott on his final trek back from the pole.

The eggs were supposed to reveal the evolutionary links between reptiles and birds but their collection nearly killed the journey's participants. They remain some of the most precious ornithological specimens on the planet and, for the first time, one will be put on public display when it will form the cornerstone of a special 100th anniversary exhibition, Scott's Last Expedition, which opens at the Natural History Museum, London.

"Ours is the world's biggest collections of eggs, with 1.5 million specimens – and many of these were brought back by individuals who went through extraordinary hardship to retrieve them," said Douglas Russell, curator of the museum's egg collection. "However, of all the 300,000 clutches of eggs we have here, the ones that generate the most inquiries from the public – by a long way – are the three emperor penguin eggs brought back from Scott's expedition. That interest is due to the fame they acquired through The Worst Journey in the World. Some people want to check we still have the eggs, others want us to admit we have lost them. Now, for the very first time, they will get their chance to see the real thing."

Scott's Last Expedition opens exactly 100 years after Scott and four colleagues reached the pole – on 17 January 1912 – only to discover that the Norwegian Roald Amundsen had got there first. All five perished on their return journey. Displays at the museum will include a reconstruction of Scott's base camp hut, expedition photographs and specimens.

However, for many visitors the complete shell from one of the eggs returned by Cherry, Bowers and Wilson will be the show's high point. "This is a once-in-a-lifetime opportunity to see the egg," said Elin Simonsson, the exhibition's curator. "Then, after the exhibition closes, it will be displayed permanently in our new Treasures gallery."

As for the other two eggs, they will be kept in storage for occasional study by researchers.

At the time of the winter trip, it was thought the emperor penguin was one of the planet's most primitive birds and that analysis of its embryos would reveal links between all birds and their reptile predecessors. However, the emperor penguin lays its eggs in June, in the Antarctic midwinter, hence the decision to make the 70-mile trip from Scott's base camp on Ross Island to the penguin colony at Cape Crozier during the worst possible weather. Scott was initially opposed to the plan, but was convinced by Wilson, the trip's zoologist, to go ahead because he thought the eggs would play a key role in understanding how species evolve.

So, at midday on 27 June 1911, Cherry, Bowers and Wilson, with two sleds of food and equipment, left base camp and trudged into a freezing, pitch-black, gale-battered nightmare. The thick, cloying snow meant they could only pull one sled at time. So they had to proceed in relay, gaining only one mile for every three they walked. The average temperature for the trip was –40C, added Russell. The impact on the men was horrific, as Cherry's biographer, Sara Wheeler, notes. "It took him 45 minutes to chip his way into his sleeping bag each night, as during the day it froze flat like a slab of tombstone granite."

Then, as they reached their target, their tent blew away and the men lay down to die. For two days they lay in their sleeping bags without food or cover until there was a lull in the blizzard and Bowers found their tent. "Our lives had been taken away and given back to us," Cherry wrote.

They reached the emperor penguin colony by climbing the huge walls of ice that surrounded it and they snatched five eggs. Cherry dropped two, but the others were returned to the team's sleds. The three staggered into base camp on 1 August 1911. Their frozen clothes had to be cut from their bodies. "Cherry looked about 30 years older than he had when he had set off, his cadaverous face scarred and corrugated, nose dark, eyes dull and hands white and wrinkled. His toenails were falling off and his fingers were useless," Wheeler notes.

Cherry was in no shape to go on the final journey to the pole, although he found the strength to take part in the expedition that set out in late October 1912 to find what had happened to Scott and his men. He was first into the tent where Scott lay dead with Bowers and Wilson. Cherry was devastated. "He had to find redemption in the journey or it would all have been a colossal waste of time," states Wheeler. "Later, after his two companions died, that thought became unbearable."

Cherry, who had no scientific training, took responsibility for the eggs and presented them to the Natural History Museum in 1913. At first a junior assistant refused to take the specimens. Then a senior member of staff made him wait in a corridor while he talked to a more important person. Eventually Cherry extracted a receipt. "I handed over the Cape Crozier embryos, which nearly cost three men their lives and cost one man his health, to your museum personally and … your representative never even said thanks," Cherry later wrote to the museum.

It became one of the infamous moments in museum history, Russell admits. In fact, another 21 years would pass before the eggs were studied and the results published. Their first recipient, Richard Asherton, of Cambridge University, had the embryos removed from the shells and slides made from them but died before he could analyse them.

The eggs were then kept in storage while occasional scientists were asked to study them. "It was difficult to find the right specialist," says Russell. Eventually, in 1934, the zoologist CW Parsons analysed them and concluded that "they did not greatly add to our understanding of penguin embryology". For good measure, scientists no longer believe that embryos help much in studying a species' evolutionary history.

However, Russell added that the specimens were used in a later study of emperor penguins and were reckoned to be useful. "Ultimately, though, they did not provide the information that was hoped for them. On the other hand, they are still here for more study and reinterpretation. In that sense, they are invaluable."

Natural disasters

The Natural History Museum egg collection has been assembled by men and women who went through extraordinary hardships to return specimens. Many died in the process.

Edward Stuart-Baker, a pioneer of Indian ornithology, had an arm bitten off by a leopard while collecting but survived by pushing it down the animal's throat. He was also tossed by a bison and trampled by a rhinoceros. He died aged 80 in 1944.

Carl Hunstein Collected several new species of birds of paradise for the Natural History Museum but was killed in 1888 in New Britain when a tidal wave swept the beach where he had camped with his collection.

John Hanning Speke During his expedition to Somalia he collected 36 bird species before he was captured by tribesmen and stabbed 11 times with spears. He escaped. Later, he became temporarily deaf after a beetle crawled into his ear and he tried to remove it with a knife.

Richard Smithwick An American ornithologist in the late 1800s, he had his career cut short when he was found with only his feet sticking out of a sandbank in Virginia, smothered to death while attempting to collect eggs from a belted kingfisher nest. He was 22.