Those coming before the MPs include David Rowland, chairman, Peter Middleton, chief executive, Sir Alan Hardcastle, chairman of the Regulatory Board, and Rosalind Gilmour, the recently appointed head of Lloyd's Regulatory Department.
They are to be asked why the regulators at Lloyd's failed to spot the huge losses run up by syndicates in the late 1980s in time to stop them. The losses were run up on the London Market Excess of Loss spiral.
The regulatory issues surrounding another sort of loss, claims from asbestos and pollution, will also be examined. Here, the business was written in the 1940s and 1950s, but claims did not hit the market until the early 1980s.
After the losses came to light thousands of new names were still put on asbestos and pollution-affected syndicates, causing them to shoulder the burden.
The market's current solvency will also be examined. Insurers become insolvent when they are deemed not to have enough assets to cover their liabilities from claimants. The arrangement with the Department of Trade and Industry allowing Lloyd's to continue trading will be probed.
There is a growing call for regulatory change at Lloyd's. All the witnesses so far have said they favour change. This includes the Lloyd's Underwriters Association, which represents all the market's agencies.