The authorities of Lloyd's believe the jobs must go within the next year or so from the hundreds of businesses that operate in the market. Falling on one of London's key financial markets, the cuts represent another blow to the City, which has suffered a substantial reduction in its workforce over the past few years.
Elsewhere in the financial services sector, declining profits are causing massive job losses. In banking, 75,000 jobs have been lost in the past three years. And the big clearing banks, suffering from huge bad debts in the recession, are expected to shed up to 25,000 more jobs over the next year.
The move at Lloyd's follows a wave of losses, totalling pounds 4.5bn in the past three years. They have brought many of Lloyd's 20,000 or so underwriting members - the 'investors' in the market - close to ruin.
Now Lloyd's authorities, led by the market's newly elected chairman, David Rowland, and chief executive officer, Peter Middleton, want companies operating in the market to follow the example they set last week when they announced 600 redundancies at the market's administrative body - a 27 per cent cut that will reduce numbers to 1,600.
It represents the largest staff reduction in living memory at the Corporation of Lloyd's, the administrative hub of the insurance market, and will bring its staffing down to the levels of the 1970s.
As a market, Lloyd's has no executive influence over the running of individual businesses within it. But under the guidance of Mr Middleton, who ran the Thomas Cook travel agency before he became chief executive, Lloyd's firms of insurance brokers and underwriters are being encouraged to cut their costs.
The job losses are unlikely to fall equally across the market. At the heart of Lloyd's, underwriting syndicates employ 4,800 people, while broking firms employ 38,000.
Thousands more are 'indirectly' employed by the market in support services. These include consultants and other specialists.
The cost cutting is a response to the intense pressure on Lloyd's to head off the anger of members facing huge losses. Earlier this month, Mr Rowland said that 2,000 members had quit the market, leaving it with just 19,700 individuals to provide the money to allow it to function - its lowest number since 1981. At its peak in 1989, Lloyd's membership stood at 34,218.
Only 67 individuals seeking to invest in the market have come forward this year, the lowest number of admissions since 1945. Of the 67 joining, 31 are professional brokers, underwriters and agents who work at Lloyd's.
Lloyd's will have made 300 of the intended 600 job cuts in its administrative body by the end of this month, according to Mr Middleton.
The administration's cost-cutting programme is intended to reduce central expenditure from pounds 144.5m to pounds 117.9m.
While Mr Rowland acknowledged that the cost savings would make little impact on the huge losses being sustained by underwriting members, he said the measures were intended to give a 'signal' to the market.
Mr Middleton is already embarked on radical plans to restructure the market's operations. He intends to remove a whole class of underwriting agent, which he believes has increased the costs of underwriting members.
He has targeted the so-called 'members' agencies for abolition. These are companies that introduce Lloyd's members to the market's insurance syndicates.