Living in the most northern permanently inhabited settlements in the world, the Inughuit people, or polar Eskimos as they are often known, have eked out an existence in this Arctic desert in the north-west corner of Greenland for centuries. The Inughuit are one of the smallest indigenous groups in the world, with a population of just 800 spread across the four settlements that make up the Thule region.

A thousand miles away from the capital, Nuuk, and occupying an unfeasibly remote corner of our world, the Inughuit enjoy their own distinct subculture based on the hunting of marine mammals. Unlike other Inuit populations across the Arctic, the Inughuit have maintained where possible their ancient way of life, using kayaks and harpoons to hunt narwhal and travelling by dog-sled in winter.

This unique way of life is now under threat. A tiny society whose basis is just a half dozen families, some of whom are descendants of polar explorers Robert Peary and Matthew Henson, say they are being "squeezed" out of existence. Draconian hunting quotas have been imposed by politicians in the south, many of whom have never ventured this far north. The hunting restrictions have pushed up the cost of sea mammals and some Inughuit are switching to a western diet of imported food.

Even if they can afford to eat their traditional diet, certain environmental groups advise them not to do so. The levels of mercury in some marine mammals are thought to pose a health hazard, and the risks of radioactive contamination from the nearby nuclear accident in 1968, when a US Air Force B-52 crash-landed with four hydrogen bombs on board, are still unknown.

The one-price policy that used to operate across Greenland, effectively subsidising the more remote settlements, has also been abolished, and the result is that the cost of living has rocketed. Local people believe the government, which has self-rule within Denmark's small commonwealth, has a hidden agenda to force out the people in the most remote communities, creating three or four urban centres in Greenland and reducing the cost of servicing such isolated settlements.

The Inughuit, however, are already a people in exile. Qaanaaq, by far the largest Inughuit settlement, was established in 1953, when the Inughuit people were given three days to leave their ancient homeland in Uummannaq, 150km (90 miles) to the south to make way for the controversial US air base at Thule. But now these displaced people face a new and unprecedented threat to their culture: global warming.

My journey to Greenland took me through pretty, picture-postcard Ilulissat in the south. Here, small amphitheatres of ice seemed to go nowhere, just sitting and collecting dirt, before sinking into oblivion. As we skirted the ice sheet, heading northwards, it seemed grey and thinning. Lakes appeared all over the ice, a tragic testament to the all too rapidly changing natural environment. It is a picture of transition, and a disturbing one: it speaks dislocation and a sense of foreboding.

A woman who has spent nearly all her life in Qaanaaq stands in my green prefabricated wooden hut, on the vast polar bear and musk-oxen skins that cover the floor. Dried, pungent blubber sits on the racks outside. Looking out across Ingelfield Bay and the whale-shaped Herbert Island, towards the exploding icebergs that sit like vast lumps of polystyrene in the Murchison Sound, there is a sadness in her eyes: "Twenty years ago, my children used to go skating on the ice at this time of the year. Just 15 years ago, the sea ice in the bay was up to three metres thick. Last year, the ice was so thin that a young hunter and his dog team of 12 fell through to their deaths. If the sea ice goes completely, there will be no need for the dogs [huskies] and our culture will disappear."

It is late September in the High Arctic, the outside temperature is -3C and there is little hope of the sea ice forming any time soon. Local hunters tell me they know it is warmer than it used to be because the dogs' breath used to be more dense in the cold. While global warming may be toasted in southern Greenland, where farmers see many benefits, it is unequivocally bad news for this tiny indigenous group.

Not only has global warming made hunting considerably more dangerous, it has also halved the hunting season. In the summer months the Inughuit hunt narwhal deep within Ingelfield Bay, using kayaks and harpoons. The narwhal leave the bay in September. The Inughuit used to start hunting seal with dog-sled at this time of the year, but that is no longer possible as the sea has not yet frozen over. A couple of years ago, the sea ice did not form at all until December and was gone again in March. In October, November and December, when the settlement is plunged into 24-hour darkness, there are few options for the hunters. The narwhal do not arrive until May, but by then the sea ice is long gone.

Like many Inughuit, this woman has relatives in the Canadian Arctic, where the Inughuit are originally from: "Previously, we used to travel across the Smith Sound to Canada on dog-sled [a distance of 40km]. Now that journey is impossible because the sea ice has disappeared."

Global warming has a human cost too, tearing families apart. To visit their Canadian relatives, these people would now have to fly to Copenhagen 4,000km away then across the Atlantic to Montreal and up from there. Air travel is prohibitively expensive in Greenland and such a journey would cost several thousand pounds, a price very few can afford. Historically, the Inughuit people were semi-nomadic, moving between the different settlements at certain times of the year for hunting purposes and to visit family.

The disappearing ice has meant that it is now too dangerous to visit the outer settlements on dog-sled, but what ice remains means that travel by boat is not an option either. Often, the only alternative is a very expensive helicopter trip. The sense of shrinking space here is almost tangible.

The threat of global warming to their traditional hunting life, alongside a host of political factors, has left the Inughuit believing that their current settlements will not be here in 15 years' time, that people will relocate southwards, and will assimilate into a broader Inuit culture. Young people, recognising that their parents are no longer able to make a living from hunting alone, are leaving the community to live a very different life in modern flats in Nuuk. Last week Moriusaq, the smallest of the Inughuit settlements, was finally closed and the others are looking increasingly endangered.

Fascinated by the Far North since I was a small child, it was about 10 years ago when I discovered the Inughuit through my reading of a book called The Snow People by Marie Herbert. This tiny Arctic community that insisted on maintaining its ancient way of life at the top of the world struck me as remarkable, and I decided I wanted to visit these people. More recently, in Cambridge, I came to understand how endangered this culture and their language was.

It is widely understood how global warming is threatening the natural environment (not least here in Greenland, with the vast iceberg that broke off recently from the nearby Petermann glacier), but the Inughuit represent a bona fide example of how climate change impacts on local cultures.

If the Inughuit are forced to leave their ancient homeland, it is likely that the language of these Arctic hunters will disappear. With it, their already endangered ancient spoken traditions – a rich depository of indigenous cultural knowledge about how they relate to the land, sea and ice, bound up in stories, myths and folklore – will also be lost.

The Inughuit are immensely proud of their language, Inuktun. While strictly speaking a dialect of Greenlandic, Inuktun is much closer to some of the Canadian Inuit dialects and the phonology is quite distinct from Standard West Greenlandic.

Working with the last handful of storytellers, I have come here to document their stories and narratives in the old Inuktun language and hope that this will act as a record of this unique and endangered culture. Rather than writing a grammar or dictionary, it is hoped that an "Ethnography of Speaking" will show how their language and culture are interconnected and how their knowledge and sociocultural experience are transmitted and performed through the filter of these spoken traditions. The stories, narratives and myths that underpin the ancient Inughuit culture will be recorded, digitised and ultimately returned to the community.

One elderly Inughuit tells me this is our last chance: "We inherited our language from our ancestors. If we lose it without record, future generations will know nothing about their rich past."

With 16 others and a small mountain of freight as co-passengers, I arrived in the community aboard a Dash 7 turboprop aircraft just over a month ago. Clouds lingered just above the brightly coloured wooden houses. Beneath were the world's most northerly people, living in a quite implausible environment.

My very first impression was the otherworldliness of the place: after four-and-a-half hours of flying up the west Greenland coast with nothing to see but bare ancient rock, meandering glaciers licking the horizon and icebergs littering the fjords, this dry polar desert with its omnipresent rocks and boulders and lack of vegetation seemed completely out of place. Sitting just 960km from the north pole, I felt as if I had come to a different world altogether rather than to the top of my own.

I had often speculated as to how I would be received into this community, and the result was quite unexpected. But I'll save that for my next dispatch…

Stephen Pax Leonard is an anthropological linguist at the Scott Polar Research Institute and research fellow at Trinity Hall, Cambridge. He will be living with the Inughuit people for 12 months. His research is funded by the British Academy and the World Oral Literature Project in Cambridge.