It is difficult to imagine a place more idyllic than the Cocos (Keeling) Islands, a collection of pristine coral cays sprinkled across a remote corner of the Indian Ocean. And for 150 years this tropical paradise was the private fiefdom of a Scottish family, the Clunies-Rosses, who imported an army of workers to carry out their bidding.

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In 1978, under pressure from the United Nations, the family was forced to sell the islands to Australia, which now administers them as an external territory. But despite their blissful surroundings – picture-postcard ivory beaches and turquoise lagoons teeming with fish – the inhabitants of the Cocos are not happy. Rebellion is stirring, with some residents accusing Canberra of modern-day colonialism.

Australia's most outspoken critic is John Clunies-Ross, the fifth-generation descendant of a Scottish seafarer who founded a dynasty after settling on Cocos in 1827. Deprived of his birthright when his father, John, gave up the sun-baked islands, Mr Clunies-Ross – who still lives there – complains that locals have no say in laws passed on their behalf.

"This place was sold on a false promise," the 53-year-old said over a beer in the Cocos Club, the islands' one pub. Mr Clunies-Ross, who occupies a modest bungalow – very different from his palatial childhood home – and makes a living farming clams, added: "We pay our taxes, but we don't have equality with the mainland. We're not even treated like citizens."

The miniature coral kingdom over which he was groomed to reign – just 14 square kilometres in total – was first spotted by an English sea captain, William Keeling, in 1609. Accidentally annexed in 1857 by a Royal Navy officer who mistook them for the Coco Islands of the Andamans, the atolls – situated 3,000km north-west of Perth – were granted to the Clunies-Rosses "in perpetuity" by Queen Victoria in 1886.

The first John Clunies-Ross, who hailed from Shetland, established copra plantations, shipping over indentured labourers from the then East Indies. He and his heirs were absolute rulers of the formerly unpopulated islands. Workers were paid in plastic money, redeemable only at the company store. The family insisted on naming every child born on Cocos. Those who left were not permitted to return.

The family also provided education and healthcare, and some old-timers yearn for the days of largely benevolent autocracy, claiming life was better then.

The copra industry died after Australia took over; 70 per cent of "Cocos Malays" – Muslim descendants of the plantation workers – now rely on welfare payments. And although their living standards have improved, they suffer from diabetes, obesity and heart disease.

The 500 or so Cocos Malays live on Home Island, one of 26 coral cays strung like fairy lights around a lagoon. The only other inhabited cay, West Island, is home to about 100 Europeans, most of them contracted by the Australian government to provide services on or for Home Island.

The pace of life in this distant pocket of the Indian Ocean is languid. The Cocos Club doubles as a cyclone shelter and airport departure lounge. The local newspaper, The Atoll, is a hand-stapled fortnightly newsletter. The crime rate is zero, unless you count riding a bicycle without a helmet, and the two police officers have plenty of time to go fishing. There is a small tourism industry, but few visitors make it this far.

The last heir to the Cocos throne defends the way the place was governed by his family. Mr Clunies-Ross – who is usually barefoot, and attired in shorts and a ripped T-shirt – said: "We looked after the community, generation after generation, pretty well. We had 100 per cent employment, 100 per cent healthcare, pensions, paid holidays – all the things people aspire to as the touchstone of social democracy. Now they have social democracy, but everything else has gone."

Mr Clunies-Ross grew up in the ancestral mansion, Oceania House, with its eight bedrooms, ballroom, spiral staircase, teak panelling and 12 acres of walled gardens, and was sent to public school in England. He was 20 when a former Australian Labor prime minister, Gough Whitlam, galvanised a UN mission into visiting the picturesque atolls. It denounced relations between the Clunies-Ross clan and their workers as "anachronistic and feudal".

Threatened with compulsory purchase by Australia, which had assumed sovereignty in 1955, Mr Clunies-Ross's father – who reportedly stalked the islands in a safari suit, a knife tucked in his belt – sold up for A$6.25m (about £10m then). He went into exile in Perth and invested the money in a shipping line, which collapsed in 1986. The Australian government had boycotted it.

According to Mr Clunies-Ross: "They wanted to break us economically as well as politically, and they didn't care if they bankrupted us in the process." Oceania House had to be sold to pay off debts, and now belongs to a former Perth taxi driver.

In a UN-sponsored vote in 1984, the islanders were offered a choice between independence, free association with Australia and full integration with the mainland. They opted for the latter, not least because everyone had been promised a new house. But while the Cocos – Australia's westernmost outpost – is Canberra's responsibility, it is also subject to Western Australian state laws. To complicate matters, it is represented at a national level by a Northern Territory politician.

Mr Clunies-Ross says Australia has yet to implement full integration. He believes "there's a deep feeling in the community of powerlessness. They feel that no one is listening to them." Noting that the Cocos's administrator is appointed by the Australian Governor-General, he adds: "We still have a colonial system."

That view is shared by Pauline Bunce, a former teacher on the Cocos and author of a book about the islands. In a letter to The Sydney Morning Herald, she referred to "the daily pattern of social and cultural interaction here, in which too many ... gin-and-tonic mainlander officials dictate father-knows-best policies to the majority Cocos islanders".

Mr Clunies-Ross is considering legal action to force a review of the integration process, which could theoretically trigger a new vote. He favours free association, which would see ownership of the land and fisheries revert to the Cocos Malays.

But while he is widely liked and respected, not everyone supports him.

Parson bin Yapat was one of two elders who addressed the UN's decolonisation committee in the 1980s. During a barbecue on Home Island to celebrate Self-Determination Day, the anniversary of the ballot, he recalled: "They [the Clunies-Rosses] pushed the workers very hard and they paid us in plastic money, so we couldn't go anywhere. We were totally dependent on them for all our services."

Home Island, which has an open-air mosque, is an enclave of devout Islam – in contrast to hard-drinking West Island. A couple of years ago, a supply ship was delayed by six weeks and West Island ran out of beer. One local recalls: "People were drinking wine, then they were drinking [pre-mixers], and finally they were drinking Crème de Menthe, and the social behaviour was getting worse and worse."

Down a frangipani-lined lane is Oceania House, with its sea views and façade of white ceramic bricks imported from Scotland. Two dozen staff were employed there in Mr Clunies-Ross's childhood.

The grounds, which are planted with almond and guava trees, have an abandoned air; behind the mansion is an old schoolhouse, covered in cobwebs, where Mr Clunies-Ross's father taught local children. He also performed medical and dental work, and presided over his own court.

His son remarks: "I can't say it was perfect. But to get 500 or 600 people all working in one direction, with a lively cultural and social life ... you would be hard pressed to find a better-run, happier community anywhere in the world."

The Cocos's nearest neighbour, 900km to the north-east, is Christmas Island, another Australian territory and the site of an immigration detention centre. While the Cocos is expensive to maintain – it costs about A$40,000-a-head annually to deliver services – it is considered strategically important. As well as being located on the edge of Asia, it has an airstrip that can accommodate large military planes.