Descendants of black American slaves are to sue Lloyd's of London for insuring ships used in the trade.
The plaintiffs say the slave trade denied them their identities
High-profile US lawyer Edward Fagan, who secured settlements from Swiss companies in the Nazi gold case, is taking the action for 10 plaintiffs.
He says by underwriting slave ships in the 1700-1800s the UK's oldest insurance firm played a key role.
The action, which claims descendants still suffer, was lodged on Monday according to Associated Press.
The American plaintiffs have produced DNA evidence they say links them with ancestors on recorded slave ships which sailed between Africa and the United States.
One says he has the insurance documents from when Lloyd's of London underwrote the ship his ancestors were on.
Mr Fagan is heading the action against several parties including Lloyd's.
He forced Swiss companies into a £1.25bn settlement on behalf of Nazi victims and is also leading a claim against companies for their role in South Africa under apartheid.
He told the BBC: "Lloyd's was one of the spokes in a hub-and-spoke conspiracy.
"Lloyd's knew what they were doing led to the destruction of indigenous populations.
"They took people, put them on board ships and wiped out their identities."
He denied events were too far in the past.
"There's ongoing injuries that these people suffer from.
"Why is it too far fetched to say blacks should be entitled to compensation for damages and genocide committed against them, when every other group in the world that has been victimised in this way has been?"
But Kofi Klu, a campaigner on slavery and reparations to the descendants of slaves, told the BBC he believed the legal action could be counter-productive.
"We have to make sure that the focus does not shift from the broad, deeper understanding of reparations to just one of financial compensation," he said.
"We see action for reparations more as an educational issue of bringing masses of people into the fight against racism - and racism is the direct product of historical and contemporary enslavement."
Lloyd's was founded in 17th Century London dockside coffee houses by Edward Lloyd.
It provided cover for merchants taking slaves and goods between Africa, the Americas and the Caribbean at a time when many vessels sank or fell victim to pirates.
Britain abolished slavery in the 1830s and the US followed 30 years later.
During the trade more than 10 million people are estimated to have been traded at West African ports and herded on to slave ships.
One plaintiff, Deadria Farmer-Paellman said the slave trade denied her identity.
"Today I suffer from the injury of not knowing who I am, having no nationality or ethnic group as a result of acts committed by these parties," she said.
Lawyers in the UK have welcomed the case.
Barrister Lincoln Crawford OBE chairs the Home Office working party on slavery and is a member of the Race Equality Advisory Panel.
He said it highlighted an important event that "cannot be glossed over".
"There is no doubt that slavery was a crime against humanity and for a lot of black people the consequences of slavery still exist today."
He said it was hard to see how they would win but added, "I would like them to".
Lawyer Fraser Whitehead, the Law Society's former head of civil litigation, said the case was not about "compensation culture".
It would be hard to prove that by insuring the merchants, Lloyd's supported the trade, he said.
"It's a bit like saying the manufacturer of guns facilitated the killing."
A Lloyds spokeswoman said: "We haven't seen this claim, so we are not in a position to comment.
"Previous claims regarding slavery involving Lloyd's have been dismissed without prejudice."