The cases of about 450 non-paying Lloyd's names were adjourned last week with both sides claiming victory in the five-year battle over whether the Names had to pay their premiums.
Dibb Lupton Alsop partner Susan Dingwall, acting for the Society of Lloyd's, said Mr Justice Tuckey had last week ordered nearly all the Names to pay their premiums with the amount to be determined in a separate hearing this week.
But Michael Freeman, of Epstein Grower & Michael Freeman, representing 450 of the names, pointed out that it was now up to Lloyd's to prove how it arrived at its calculations of the amount it said the names owed.
"The judge said it was up to Lloyd's to prove the basis of its calculations under the Equitas contracts clause 5.10," he said. "We're not convinced Lloyd's will ever be able to produce anything that will satisfy the judge."
Freeman added that Lloyd's had also not been successful in getting his counterclaim of fraud dismissed last week. "Lloyd's have until 31 January to file a defence to the counterclaim alleging fraud since 1980," he said.
But Dingwall remains confident: "I suspect it is the end of the road for those names who have so far refused to pay," she said.
A handful of other names, represented by other lawyers, got their cases adjourned to be dealt with separately because they raised other legal points.