Proxies lodged ahead of a meeting, attended by 500 of the 3,000 Gooda Walker Action Group members at the Grosvenor House Hotel in London, showed more than 90 per cent in favour.
The final count is expected this morning but is likely to show a similar out-turn. The tally of proxies and votes received early in the day was 1,100 in favour and 120 against.
A vocal group of several dozen members, led by Howard Johnson, an American member, warned the meeting that members were being conned into a disastrous settlement and complained about conflicts of interest on the action group committee.
They campaigned unsuccessfully to force the action group's chairman, Michael Deeny, to quit his membership of the Lloyd's ruling council and also attacked the success fees which are to be paid to action group committee members.
These payments will be based on the recommendations of an independent remuneration committee. Motions put forward by the rebel members to change the way the success fees are to be paid were heavily defeated.
Mr Deeny told members that lives had been blighted by what had happened to the Gooda Walker syndicates and some of the committee would have liked to see the perpetrators in jail.
But attempts to pursue them through the Serious Fraud Office had not worked. The action group committee strongly recommended acceptance of the Lloyd's proposals.
Action groups must formally agree to withdraw their legal actions against Lloyd's as a condition of the reconstruction and renewal programme. But their individual votes on whether to accept are due to be posted over the next four weeks, up to a deadline of 28 August.
Many members should today receive their detailed "finality" statements.