The letter, written to a name and signed by a senior civil servant at the DTI, implies that names, the individuals whose private wealth supports the market, could face a cash levy within the next few months.
It refers to the two annual solvency tests that Lloyd's must pass: the market-wide "global" test and a second one.
The letter reads: "Lloyd's is also subject to a second solvency test that the names separately must demonstrate that their insurance assets exceed their insurance liabilities. This test stands alone and is a precondition to the global test. This test is giving rise to some difficulty."
The letter also says that the problem can be resolved "by some well-known solutions within Lloyd's gift" - a reference to the need for a levy on the market's members.
The admission by the DTI that Lloyd's has a solvency problem is a reversal of the position it took at a hearing of the Treasury select committee in February.
The problem arises because of non-payment of losses by approximately 7,000 insolvent names. A name is insolvent at Lloyds when underwriting losses exceed his or her known assets.
At 2 September last year, this group of 7,000 had liabilities worth £1.35bn more than their assets. This figure is understood to have fallen to only £1.1bn by early 1995. European insurance law requires that the Lloyd's market maintains sufficient assets to cover this shortfall. It appears that the DTI now believes this will not be the case at the time of the next solvency test in late August.
It is understood that Lloyd's is to link the call for more cash from names with the offer of an amnesty on all future losses arising out of business written before 1993.