The move was sparked by fear that names would refuse to use any court awards to pay their Lloyd's liabilities.
David Rowland, Lloyd's chairman, said that the planned amendments had been given urgency by a recent court judgment that any awards to Lloyd's names be made on a "first past the post" basis.
That means that when the errors and omissions insurance cover held by the agents being sued runs out, names who are further down the litigation ladder would lose out because there would be no money left to pay any awards.
The High Court also began hearing an application by the Gooda Walker names for an interim award following their win in the courts last year. The damages they are entitled to are estimated at more than £500m.
Lloyd's first proposed amending the premium trust deeds in October, but shelved the plan in the face of fierce opposition from names and in the hope of agreeing an overall settlement with all the litigating names before any awards were made.
In a letter to names explaining the move, Mr Rowland attempted to reassure them that a settlement was still being pursued.
"We still believe a settlement offers the best chance of a fair resolution of the disputes," Mr Rowland said.
"We shall continue to work to achieve this. But in the meantime, Council have concluded that, because circumstances affecting litigation recoveries have changed in the past two months, it is necessary now to seek the Secretary of State's consent."
Michael Deeny, chairman of the litigating names' committee and of the Gooda Walker Action Group, said: "Lloyd's explanations lack credibility. It has been known that there would be a Gooda Walker application for an interim payment since October. The decision in favour of `first past the post' was widely expected and the Lloyd's underwriters involved in the case actually argued for this principle.
"No settlement negotiations have taken place since Lloyd's announced the proposed changes. One has to begin to question the sincerity of Lloyd's interest in a settlement of the litigation."