Equipped with ingenious contraptions such as the magnificent Boat-Cloak – an inflatable dinghy that doubled as a cloak, powered by a sail that could be used as an umbrella – Victorian adventurers set out on a perilous quest: the search for the Northwest Passage.

A new exhibition at the British Library focuses on this hunt for a navigable channel that explorers believed connected the North Atlantic and the Pacific Oceans. The show includes maps, photographs and manuscripts tracking more than four centuries of avarice and arrogance, from the mythical frozen gold mines of Tudor times to today’s pursuit of oil under the rapidly retreating ice cap.

Curator Philip Hatfield has pointed out the similarities between recent satellite images that show stretches of clear dark sea in the Arctic ice, and early maps that depict a shortcut that would allow ships to sail over the top of the world instead of crossing thousands of miles of ocean.

The exhibition includes a wonderful atlas made for Charles II, one of whose scientists insisted that open stretches of salt water could not freeze – an error that generations of sailors would discover to their cost.

Another of the maps, presented in parliament in the 18th century, led to a £20,000 prize being offered for the discovery of the Northwest Passage. It turned out that most of the chart was fictitious, as Captain Cook learned when he found himself sailing for weeks around a land mass that it did not show.

Preparation work on the exhibition was almost complete when Canadian scientists found the wreck of HMS Erebus – the ship that belonged to Sir John Franklin. In 1845, Franklin set sail from Greenhite in Kent with two ships, Erebus and Terror. Both eventually became locked in the Arctic ice and the disastrous decision was taken to abandon the ships and seek safety on foot rather than waiting in them until the spring thaw. Franklin and all 129 crew members were lost.

“When I heard of the project, I thought they might find something really interesting like a Franklin spoon,” says Hatfield. When I heard they’d got the ship, I was staggered.”

The exhibition includes a letter from Lady Jane Franklin, who refused to lose hope for her husband and his men. She bombarded the government with demands for a rescue expedition and raised funds for the search. John Rae, a man from Orkney with experience of the Arctic and a deep respect for the knowledge of its native people, took up the challenge.

Rae brought back evidence, including some personal possessions purchased from the Inuit, that Franklin was undoubtedly dead, and that some of his men had been reduced to cannibalism before dying of starvation. Lady Franklin refused to believe that British heroes could ever have resorted to such behaviour. Her supporters included Charles Dickens, who wrote a number of pamphlets condemning Rae’s reports. Rae – who did actually try out the magnificent boat-cloak – is now an almost forgotten figure, but he is commemorated by a beautiful memorial in St Magnus Cathedral in Orkney.

“To me, Rae – in his respect for local knowledge and skills, and the advantage of travelling lightly and living off the land – relates to Roald Amundsen, whose achievements were also denigrated by the British,” says Hatfield. Amundsen, who beat Captain Scott to the South Pole, learned his survival skills at its northern counterpart. The show includes archive film of him joining the first attempt to fly an airship across the Arctic in 1928.

Hatfield has also tried to include voices that have long been left out of the story: those of the local people. There are images of local customs drawn by an Inuit artist and printed by a 19th-century missionary who set up the first printing press in the Arctic, and maps including beautiful pieces of notched wood that outline bays and headlands. There is also an extraordinary recording, made in the late 20th century, of an Inuit woman speaking of an encounter as if it had happened the previous week. The story she tells has been handed down orally for generations and details how her ancestors met the explorer Sir John Ross 170 years earlier. Apparently, they were initially alarmed by a peculiar smell that was blowing in on the wind and driving their dogs crazy. Their shaman told them not to worry, it was just the smell of white people, and harmless.

• Lines in the Ice: Seeking the Northwest Passage is at the British Library in London, free, until 29 March.