The great unofficial census of Eigg is taking place in a sitting room offering the UK’s finest seascape. The waters of the Sound of Rum carry your gaze from beyond a spotless beach on the north-west side of this island – one of the Small Isles of the Inner Hebrides – and bring it to rest upon a phalanx of peaks belonging to Eigg’s larger sister, Rum.

Peggy Kirk, the universally acknowledged matriarch of this isle of 100 souls, has counted them all in and yet more out. Today she is joined by her friend Mairi Mackinnon, who runs a croft a few fields down. It was revealed last week that the population of this kenspeckle, but remote, island off Scotland’s west coast had stolen over the 100 mark for the first time in half a century and reached 105 before anyone noticed.

Peggy, the fount of accepted wisdom on Eigg, and Mairi hesitantly confirm the figure and then, for the benefit of this one-man press corps, name them all: road by road; house by house; croft by croft; every man, woman and child. “Yes, we can officially confirm that the total is 105,” Peggy says; her smile as good as a wink.

At the head of the pier where the CalMac ferry once a day disgorges its cargo of people, cars and supplies, it seems that half of the adult population are gathered. The talk is of an American film news team who will soon arrive on the island to make a programme for the CBS 60 Minutes programme. They are one of several international broadcasters keen to mark the 20th anniversary in June of the famous Eigg Community buyout. Maggie Fyffe, 41 years resident on the island, is secretary of the Isle of Eigg Heritage Trust, the body that owns the island and finally succeeded in taking it out of private ownership in 1997.

She is a veteran of the battles with Keith Schellenberg, the Yorkshire-born motoring magnate who bought the island in 1975 with good intentions but quickly turned into a medieval-style feudal baron as he reneged on a multitude of promises to grant long-term leases to families on his estate. As his relationship with the islanders disintegrated, he refused to make essential repairs to properties while prohibiting tenants from carrying them out.

The islanders eventually saw him off the premises but not before the landowner, by now a reviled figure, attempted one last act of sabotage in 1995 by selling Eigg to an unknown German artist. It soon became clear that he had a mottled financial history and the Heritage Trust knew they had to gain ownership and a global fundraising campaign, supported by the Highland Council and the Scottish Wildlife Trust, got under way. The buyout was concluded for £1.5m with almost the entire amount donated by members of the public, including a mysterious woman who gave £750,000.

About 500 individuals currently own more than half of Scotland; a pattern of land ownership that ongoing land reform legislation is attempting to unstitch. The Eigg experience since the buyout is a powerful rebuke to the owners of Scotland’s big estates who insist that much of their land is rough terrain; that it is unfit for human habitation and that only they have the expertise learned over centuries to manage it appropriately. What has been achieved on Eigg, a 12-square mile expanse of cliffs, fields and high, whipped winds would suggest otherwise.

The trust set about the task of building a management and social infrastructure to ensure that the islanders would always be involved in decisions affecting their community. The transformation of Eigg since the buyout has been astounding. The population has grown by more than two thirds and properties have been renovated, leading to more employment opportunities and a steady increase in living standards. A sound broadband network is in operation and with it an island website, which has provided small businesses on Eigg with global marketing and tourism opportunities. The electricity grid is entirely run off renewable sources.

When you make your way off the ferry you immediately come upon the hub of this island community, with a shop, post office, tea-room and craft outlet. Here, each day, islanders come down to meet the boat and engage with each other. There is a palpable sense of community in which people solicit their neighbours’ expertise or wisdom. New arrivals are soon included; the room doesn’t fall silent and sullen when an incomer swings by. Instead there is an offer of tea and transport on an island where visitors are gently discouraged from bringing cars.

Maggie can see only good things ahead. “Look,” she says, “I don’t want to depict this as some kind of political and social utopia. We are a rum bunch with as many bumps and warts as any community, but clearly we are doing something right. Young people who grew up here or who visited here are returning with their partners and children.”

Looking towards An Sgurr (The Notch), on the Isle of Eigg. Photograph: Alamy

In 2014, the islanders voted by a factor of more than nine to one in favour of Scottish independence. “I don’t think this was down to any great affinity with Scottish nationalism,” said Dougal Tolan, a Londoner who came here three years ago seeking volunteer farm work and now finds himself the resident sound engineer at Eigg’s regular live music events. “We voted for something that we had already achieved. We had thrown off a system where nothing could be done without prior approval to one where anything and everything was possible and we couldn’t blame it on an absentee laird.”

The shadow of Brexit also hangs over Eigg. There are three sheep farms here, reliant on European grants, and European money has also made possible several key developments in the last two decades such as the new pier. Future developments may have to rely on expanding the tourism infrastructure, which will entail road improvements and expansion of the electricity system. The community though, as the buyout showed, has become proficient at finding funding. The experience of Johnny Jobson, a journalist on a major newspaper now working remotely from Eigg, is emblematic of the island’s renaissance. A keen diver, he visited this place 25 years ago for seasonal work with a fellow member of his diving club who had moved here. Having then married and raised a family in the Glasgow area, echoes of his childhood came flooding back and with them an old yearning. “It was the smell of a wood fire in my new neighbour’s home that did it,” he said. “So my wife and I and our three children began making Eigg our annual holiday destination and my children fell in love with it just as I once did. Two years ago we took the decision to return permanently.

“Both of us worked very hard – me as a journalist and Jackie as a courtroom lawyer – but I felt we were running up a down escalator and that we just weren’t spending enough time with our children. Here, they are getting an excellent education on the island primary school [three teachers, five pupils] and Mallaig Secondary across the water [140 pupils, five pupils to a class]. We never worry about what they are doing, the company they are keeping, their whereabouts. They are getting a free-range childhood.”

Ben Cormack, the father of newborn Oran, was himself born and brought up on Eigg. After living in Glasgow for a decade or so, he felt the island pulling him back. “There is a deep sense of belonging in this place that remains with you wherever you go. I loved Glasgow’s big-city atmosphere and its vibrant food and music scenes, but Eigg gives you a sense of time and place that never leaves you. My wife Gill has said that she sees this in all my friends who came from Eigg and wanted to experience it too. I know our son will be happy here and it will always be a part of him wherever he goes.”

At 86, Peggy, who has lived here for 58 years, is the oldest resident. From her front room, you can see baby Oran’s home perched upon the last expanse of pasture before it dips towards the sea. The first and the last; the youngest and the oldest separated by one field and three generations but linking Eigg’s turbulent past to a promising future.