Beazley has launched a bid to buy out the Names that back its specialty lines Syndicate 623, but some private investors have slated the offer as "derisory".
The Lloyd's managing agent has offered Names 2.7p for every pound of capacity they provide after it exceeded the 75% aligned capacity limit in the 2006 year of account.
Under capacity offer rules set down by Lloyd's, when a managing agent owns over the 75% threshold it is obliged to make a mandatory offer to buy out third party investment.
Andrew Beazley, chief executive of Beazley, admitted that he would be "very surprised" if the group succeeded in its buy-out bid, but defended the offer price.
"Many [Names] wish to remain members of Lloyd's," Beazley told Insurance Times.
He said: "What is the right price? In essence, you are only buying the right to participate in future years. You are not buying pipeline profits.
"It depends on what your view is of the insurance industry and what it is worth to buy that right. But we are in the risk business, so the price is slightly in the eye of the beholder."
Beazley said if the bid were not successful, then it was unlikely to impact on the syndicate, as it would continue to write the same business and charge Names the same fees and profit commissions as it does now.
Names contribute £189m to Syndicate 623, which specialises in professional liability, product recall and directors' & officers' liability insurance.