It is located on the former site of East India House in Lime Street, in London's main financial district, the City of London. The building is a leading example of radical Bowellism architecture in which the services for the building, such as ducts and lifts, are located on the exterior to maximise space in the interior.

The first Lloyd's building (address 12 Leadenhall Street) had been built on this site in 1928. In 1958, due to expansion of the market, a new building was constructed across the road at 51 Lime Street (now the site of the Willis Building). Lloyd's now occupied the Heysham Building and the Cooper Building.

Twenty-five years after completion in 1986, the building received Grade I listing in 2011; it was the youngest structure ever to obtain this status. It is said by Historic England to be "universally recognised as one of the key buildings of the modern epoch".

The building was previously owned by Dublin-based real estate firm Shelbourne Development Group, who purchased it in 2004 from a German investment bank. In July 2013 it was sold to the Chinese company Ping An Insurance in a £260 million deal.