The deal provides for Cape to pay 11 million pounds in a lump sum and a further 10 million over 10 years. Cape will also pay the claimants' 2.25 million pounds in legal fees, though the company said in a statement it did not admit liability.Cape's own legal costs are estimated to be substantially more than that.
The agreement means the claimants put their court battle on ice while the parties work to meet its conditions. It is conditional on the ability of the company to raise the money and the setting up of a trust to administer the cash, with lawyers for the company and the claimants cooperating.
They have a six-month deadline to finalise the matter.
Lord Brennan, acting for the claimants, told the court it was a historic agreement, being the largest group action ever to go before the British courts and also the largest transnational claim of its kind.
About 7,500 claimants, who blame Cape for diseases contracted at the firm's asbestos mining operations in South Africa's Northern and Northern Cape provinces, could be entitled to a share of the payout.
Asbestosis destroys the lungs and eventually kills its victims, and can take decades to become apparent.
Chris Matlhako, spokesman for the Northern Cape province, said the agreement offered a glimmer of hope to the sick and those who had lost relatives to disease, as well as those who could still fall ill in future.
"The victims should feel vindicated. They have waited patiently for this moment and they will be rejoicing," he told Reuters.
"The next step for us to do, is to put in place as quickly as we can, ways of increasing the claimants' ability to get a better life," he said.
"This (agreement) further produces the possibility of exploring other ways of providing specialised healthcare to those who are in critical condition, to prolong their lives as far as we can."
Cape, which makes fire protection, insulation and building products, no longer uses asbestos.
Its shares were trading unchanged around 18 pence last week, valuing the firm at about 9.78 million pounds ($14 million) - less than a tenth of the company's value in mid-1994, when its shares traded at almost 280 pence each.
"This is an important development in the recovery of Cape," said company Chairman Paul Sellars in a statement.
"Ending this litigation will enable the board to look forward to the future."
SLOW DEATH
Asbestosis is caused by the fibres in the substance, which scar the lung, making it hard and inflexible and causing severe shortage of breath. People can also develop deadly cancerous tumours from inhaling the fibres.
Cape had already settled claims by workers at operations in Britain. The firm closed a factory in Barking, east of London, in 1968, after workers developed asbestos-related diseases.
But it kept its asbestos operations going in South Africa until 1979. Four years later asbestos was declared a hazardous substance and South Africa began closing down mines.
Cape had wanted the claims to be heard in South Africa, but the House of Lords ruled last year that they could go before a British court. A trial had been scheduled for April 9 next year.
Lawyer Richard Meeran, acting for the claimants, said the central point of the case was making sure that multinational companies should be held accountable for their actions.
He said companies like Cape should not be able to wriggle out of their liabilities by using separate legal identities such as foreign subsidiary companies.