But in a surprise late demand, Mr Nelson insisted that Lloyd's give an assurance that it is prepared to find up to pounds 100m in the period to January 2002, to top up the pounds 1.68bn reserves of Equitas, the new reinsurance company at the heart of the rescue.
Mr Nelson said the pledge was required in case interest earnings on Equitas's investments were lower than expected or there was a shortfall in contributions from agents or brokers.
David Rowland, chairman of Lloyd's, said: "Our regulators have driven hard bargains all the time."
He described the extra money as "one more piece of belt and braces that the DTI thinks necessary". But he declined to say whether the names who are members of the market would have to pay.
Mr Rowland was speaking after presiding over a variation on the celebrated Lloyd's ceremony of ringing the Lutine bell once for a disaster and twice for good news.
The first of the three rings was a reminder of the pounds 8bn losses at Lloyd's and the other two were to announce the good news of the rescue.
Mr Rowland said: "I wanted to mark the difference. Once for sorrow and twice for joy was in the history of Lloyd's. This is a very special occasion.
"The most important thing for the market to remember is how close we came to not surviving, and the reasons for it," he told a packed meeting of thousands of Lloyd's professionals in the underwriting room in the insurance market's headquarters in Lime Street, to loud applause.
The bell has been rung more than twice on a previous occasion, though that was when it was rung four times in 1994 for the performance of a specially composed piece of music. The last time it was rung twice as a result of good news from the ocean was in 1981 when an overdue Liberian ship was found.
And the last time it was rung once for a maritime disaster was when wreckage of the tanker Berge Vanga was found in the South Atlantic in 1979.
As a result of the completion of the rescue, Equitas is to re-insure all Lloyd's pre-1992 liabilities, which were pounds 14.7bn at the end of last year.
Claims payments since then have reduced the total to about pounds 11.5bn.
Mr Nelson said that since he conditionally authorised Equitas in March there had been an overall strengthening of its financial position.
The process of transferring money to finance these liabilities can now proceed, including trust funds held in the US by the New York Insurance Department, which has also agreed the rescue and is to continue to be given Lloyd's financial data to monitor. Yesterday the department approved a transfer of pounds 3.5bn.
Mr Nelson said there would be a review of Lloyd's regulation, but it would be deferred until after the election. He expected changes to be made to the whole system of financial regulation and any reforms at Lloyd's would have to be studied in that context.
Mr Nelson is to introduce new regulations in Parliament shortly which will clarify the regulatory position for names who wished to leave the market but have been unable to do so until Equitas starts operating.
Lloyd's is expected formally to pass its annual solvency test at the DTI in the next few days.