Lawyers acting for Mr Donner have prepared writs making the same allegations, which are on hold until after the meeting with Sir Alan.
An inquiry in 1989 found no evidence of wrongdoing by the market's authorities.
Mr Donner alleges that leading market figures knew the insurance industry was facing huge claims from victims of asbestosis in the United States, but they withheld the information from the rest of the market. Subsequently many thousands of new names joined the market only to be hit by huge asbestos- related losses.
Mr Donner claims that he has new evidence not made available to the 1989 inquiry. In particular, he has a document sent by Lloyd's US lawyers to the late Don Taylor, who was chairman of Lloyd's asbestos working party in 1982.
This document warns that the cost to the industry could reach dollars 170bn.Reuse content