A legal activist in the US has made a landmark step this week by filing a lawsuit against insurer Aetna and several other US companies - accusing them of profiting from slavery.
If the case is successful, Lloyd's is thought to be a prime target for future actions as it is likely to have insured the ships that transported slaves in the 19th century.
However, Lloyd's said in a statement that it has not been contacted by anyone in this regard.
It also explained the difficulties of bringing such a case, saying that the businesses that made up the Lloyd's market at that time no longer exist, and the majority of their records have been destroyed.