However, there has been an immediate climbdown by the market over a writ issued against Flight Lieutenant Harold Selway, a name who says he has already paid everything he can to the market.
More writs are expected to follow in the next few days, with the total number being sued rising to 25. Lloyd's has said that the writs are being issued as a last resort. A spokesman said: "We have explored every other avenue to settle these debts amicably."
The action against the names represents an about-turn of a policy introduced at Lloyd's in late 1992 when Peter Middleton was appointed chief executive. He then announced a moratorium on further legal actions to recover debts.
Since then the level of nonpayment by names has escalated to a point that it is now threatening the ability of the market to continue trading.
On Tuesday Lloyd's announced a rescue package designed to restructure and refinance the market.
Christopher Stockwell, chairman of the Lloyd's names associations working party, said: "It is disgraceful that at a time they are trying to negotiate a settlement they take this action to sour the climate."
On the climbdown over Flight Lieutenant Selway's writ, Mr Stockwell said: "This shows what a mess they are making of this."In the past Lloyd's has said that it has received support for pursuing those that can't pay by thousands of names who have met their share of the losses.