But the final building block for the reconstruction and renewal plan cannot be put into place until next week when Anthony Nelson, the trade minister responsible for the market, returns from holiday.
He must approve the setting up of Equitas, the pounds 14bn reinsurance company taking over Lloyd's liabilities for asbestos and pollution and other losses up to 1992, ring-fencing them from the rest of the market.
Mr Nelson gave conditional approval to Equitas in March, and must now remove those conditions before the assets can be transferred from Lloyd's to the new reinsurance company, which is expected to start conducting business during September. A key condition was that Lloyd's members approve the rescue plan.
Immediately after yesterday's meeting of the 16-strong council, Lloyd's met DTI officials to brief them on progress ahead of the Mr Nelson's decision.
Meanwhile, the Paying Names Action Group - representing members who paid their losses on time but who got worse terms than those who refused - wrote to all members of the council, asking them to consider some form of extra compensation after the rescue goes through.