The claim follows a High Court ruling that laid out the principles by which any maximum compensation is to be calculated.
The names on the Gooda Walker syndicates ran up £1bn of losses between 1988 and 1990. Last October a High Court judge decided they were the victims of negligent Lloyd's agents.
The same High Court judge, Mr Justice Phillips, has now decided on the principles for calculating the names' award. The two sides in the case, the names and the agents' insurers, are in the process of agreeing the figures to be derived from the principles outlined in today's ruling.
The names expect total damages to fall between £435m and £561m.
The judge has decided the names are entitled to the losses they have paid so far and the names say this is worth £267m to them.
The judge has awarded the names interest on sums to be paid out in compensation, which the names say is worth £87m. However the solicitors for the agents insurers deny that any figure for interest has been agreed.
The settlement is not to be full and final, so names will be able to go back to court in future years to claim damages for any losses not yet reported by the Gooda Walker syndicates.
The judge decided it was too difficult to assess the level of future losses and related damages immediately. But the names estimate that the damages they will receive for future losses will be between £61m and £172m.
There will, the names say, also be £20m-£35m in other damages payable.
Michael Payton, the solicitor for the agents' insurers, cast doubt on the size of the payment to be paid to names. Mr Payton said: "No figures have been agreed. The interest is to be the subject of further hearing on May 10 and there are fundamental differences on this. They have specifically not been given an indemnity."
Mr Payton said the names would receive no money at all until after further hearings had been completed.
The Court of Appeal is to decide at the end of this month on whether Gooda Walker names can be paid now or must wait until after all Lloyd's litigation has been resolved - a process that could take till the end of the century.Reuse content