St Vincent and the Grenadines. A string of islands that stands out in Caribbean holiday brochures as the destination with the most turquoise of waters, the most pristine of white-sand beaches. Home to the ultra-exclusive private island and celebrity hangout Mustique. Yachting paradise. A population of only 110,000.

Now it is becoming the perhaps unexpected centre of a pan-Caribbean move to redress one of the great horrors of the 19th century: the transatlantic slave trade.

"It is the defining matter of our age," says the prime minister, Ralph Gonsalves, as he peers out towards the Atlantic from the veranda of his family's secluded villa, in the grounds of an old plantation, on the main island, St Vincent.

The outspoken 67-year-old, who often refers to himself as "Comrade Ralph", has been in office for almost 13 years. He says his attempt to seek not only an apology but money from those European powers that built fortunes through the trafficking of slaves across the ocean in front of him is his moral duty. And it is one he pledges to devote his energies to as he prepares to assume the leadership of Caricom, the organisation that unites the key Caribbean states.

"We believe we have the facts on our side. We believe we have the law on our side," he tells the Observer. "International law is there to resolve disputes between strong states and weaker ones."

For several decades, activists, academics and cultural leaders have sought compensation from European governments for the role they played in taking slaves from central and west Africa, packing them in gruesome conditions in ships and forcing those that survived the journey to work in the hugely profitable sugar plantations of the Caribbean.

To date, those efforts have not succeeded. But last June supporters of the reparation movement were emboldened by a £19.9m out-of-court payment made by the UK to victims of British colonial forces in Kenya. Lawyers had argued that Britain was legally responsible for the brutal suppression and torture carried out against the anti-colonial group the Mau Mau in the 1950s. The foreign secretary, William Hague, publicly expressed regret for the abuses, although the UK government never formally accepted responsibility for the actions of the administration in Kenya.

Now Gonsalves has instructed Leigh Day, the same London law firm that acted for the former Mau Mau, to represent Caricom in a joint action against the UK, France and the Netherlands. He says that, while other countries may have been involved, the European countries cited were "the main culprits".

Martyn Day, senior partner at Leigh Day, acknowledges that this threatened litigation is far more complicated than the Kenyan case. Crucially, it does not involve living individual claimants, who could be presented to court. Both the perpetrators and the direct victims are long dead. But Day insists that it is a very carefully considered undertaking. "The western powers should be under no doubt as to the seriousness of the Caribbean nations about this," he says, adding that he believes the international court in The Hague could, if necessary, hear the case.

As yet, no formal claim has been made or case compiled. But all 15 heads of government in the regional Caribbean grouping have agreed to participate. Each country has set up a reparation committee, tasked with the seemingly impossible challenge of assessing the long-term financial cost of both eliminating native peoples and slavery.

Their argument, which comes at a time when many Caribbean economies are still struggling to recover from the 2008 economic downturn, is that the legacy of under-development is tangible. St Vincent and the Grenadines gained its independence in 1979. "In 200 years, the British built just two schools in St Vincent. One for boys and one for girls," says Gonsalves. "In nine years, I have built 10."

Neither Day, nor Gonsalves, is prepared to speculate about how much they will seek in reparations. But Gonsalves refers to what he sees as a possible precedent. In 1833, after the abolition of slavery, the British parliament authorised a £20m payment to British plantation owners, the equivalent of £16.5bn today. This was deemed appropriate compensation for their loss of "property", meaning slaves. The slaves themselves received nothing. A University of London report published this year lists the individuals who received the payouts. Several prominent families, including a very distant relative of David Cameron, were among the beneficiaries.

Gonsalves is the most vocal proponent of reparations among Caribbean leaders, despite one anomaly that he describes as being the subject of "whispers" among European diplomats.

The prime minister is the descendant of indentured Portuguese servants who came to St Vincent in the 1840s. He has no apparent African blood. He laughs off the suggestion that his ethnic background is relevant. "I am a Caribbean man," he says.

Not all on these islands are convinced that seeking compensation for crimes committed more than 200 years ago is realistic or even desirable. A short ferry ride from St Vincent is the even smaller island outpost of Bequia. Its large horseshoe harbour is a popular stopping-off point for yachts cruising the eastern Caribbean. The island's oldest hotel is owned by Sir James Mitchell, the second prime minister of St Vincent and the Grenadines after independence who served for a total of 16 years.

Mitchell, 82, rolls his eyes when the subject of reparations comes up. He describes slavery as an "abominable exercise" but says that time, and history, make seeking any compensation for its legacy hopelessly impractical.

"Look at someone like me," he says, "I have a genealogy that is mixed of Africa and Britain. So, am I going to pay, or receive, some of that money? And what about the West Indians living in the UK? Will their taxes be paying for this? Is that fair?"

He also points to the millions of pounds the country receives in UK and EU development aid. "The road to the prime minister's house was built by the European Union," he says.

Curtis King, a historian and teacher who is on the St Vincent reparations committee, believes that focusing on the idea of cash payouts is missing the point. "The idea is not to try to get a big cheque and dish out money to all and sundry," he says. "We are looking for the establishment of a developmental fund that will benefit the country. We are looking for something mutually agreed upon with the British, to bring closure to a period in history."

Britain is opposed to the principle of reparations. A Foreign Office spokesperson said: "The UK unreservedly condemns slavery and is committed to eliminating it. We do not see reparations as the answer."

On Sunday evenings outside Kingstown, local musicians gather to play in open-air concerts by Mount Wynne's black sand beach. Calypso star Glenroy "Sullé" Caesar composed a song called Reparations, which has since become an anthem of the movement. "Reparation doesn't totally and necessarily mean financial compensation," he says. "It is about recognising a wrong, about recognising that slavery was an injustice against humanity. And about us retrieving our history."

Day said one concrete claim for which countries were considering requesting funding was a world-class museum in the Caribbean to explore the history and legacy of slavery. "It is noticeable that there is not a single such institution in the region," he says.

Gonsalves, who is widely expected to be seeking a fourth term in office next year, insists he does not want to fall out with Britain. "You are not going to see me in front of No 10 Downing Street with a placard," he says.

"I'll have a letter delivered to the British prime minister, at the appropriate time, for serious negotiations to begin. We have to right these historic wrongs."