Lloyd's faces a multibillion-dollar lawsuit for financing of trade ships used to uproot and transport black African slaves in the 17th and early 18th centuries.
So far, no legal papers have been served, but Lloyd's denies that it is liable and is confident of its position.
A Lloyd's spokeswoman said: "This complaint is based on the same factual allegations as the cases that were recently rejected in Chicago. We completely reject the allegations."
The suit will be fraught with difficulty for the claimants. Previous allegations proved fruitless, as plaintiffs were unable to produce sufficient evidence. Ten people claiming to be descendants of the black American slaves are filing the current action. The claimants will be represented by Edward Fagan, known for having represented holocaust and South African apartheid victims.