The Association of Lloyd's Names said this could prevent otherwise solvent members from staying in the market to benefit from the bumper profits of 1993, as well as causing needless worry to names who had already been forced out of the market by losses.
The ALM said the Lloyd's assessment in part represented 'fictitious losses which do not exist and will never have to be paid'.
The claim was rejected as false by David Rowland, Lloyd's chairman, in a letter to the ALM, which he accused of causing unnecessary confusion and concern to the members, or names, and raising false expectations of what could be done to change the situation.
But Mr Rowland's letter to Sir David Berriman, chairman of the ALM, appeared to confirm at least part of the claim that assessments of solvency are on the pessimistic side.
Solvency measures names' ability to meet their financial commitments and depends on assessments of past and future finances. Only names who pass a minimum standard of solvency can continue in the market.
The letter appeared to concede that the official figures could be up to pounds 900m too pessimistic. Mr Rowland said the discrepancy was probably less than a third of the pounds 2.67bn the ALM suggested.
This ALM figure was in the draft the names sent Mr Rowland for comment. Robert Miller, who researched the issue for the ALM, said he had reduced his estimate from pounds 2.67bn to pounds 2.05bn after accepting one criticism of his figures made by Mr Rowland. But he stood by his other calculations.
Mr Miller listed a series of anomalies that he said 'will prevent otherwise solvent names from continuing to underwrite, either at all or at a lower level than should be possible.'
Mr Miller said the pounds 2.05bn was made up from six different areas. There was a pounds 500m double count, already admitted by Lloyd's, caused by the fact that some names were insuring other names for losses due to errors and omissions by their syndicate managers.
But there was a further pounds 200m exaggeration of costs to be found in unrealistic solvency deficiencies in the 1992 and 1993 accounts, plus pounds 350m for 1991 and previous years.
To this Mr Miller added pounds 300m that he believed was a further double count of names' liabilities in the so-called LMX spiral in which business was passed around the market, leading to heavy losses. Mr Rowland admitted there may be some double counting but said the figure was sheer speculative guesswork.