The deal removes Equitas’s last large asbestos exposure. Babcock & Wilcox, which is currently in Chapter 11 bankruptcy protection, used the deadly fibres to insulate its giant boilers.

Since 1996 Equitas has paid out more than $7 billion in asbestos settlements and £16 billion in total claims. The settlements allow Equitas to cut off its liability to the policyholder and to reduce the fund’s costs.

“This is at least a year’s work,” said Scott Moser, chief executive of Equitas. “A settlement is a favourable outcome [because] we’d rather pay claims than lawyers.”

Mr Moser said that by paying a lump sum to remove one of its largest exposures, the risk to the whole fund had been reduced. Such settlements are also known as “policy buyouts” or “buybacks”.

Mr Moser said: “Every time you’re able to put one of your biggest ones to bed at a price you can afford, you reduce the residual risk of having a claim you can’t afford.”

It was the first settlement that the fund had negotiated directly with representatives of asbestos victims, rather than with a company itself.

Equitas was created in 1996 to cover the huge liabilities that Lloyd’s insurers accumulated in the 1960s, when asbestos use was rife, and the 1980s, when insurers were hit by a series of natural disasters.

Estimates for the total bill facing the fund have been as high as £42 billion.

In the past two years the fund has agreed 11 major asbestos settlements worth $2.2 billion (£1.7 billion), including pacts with big construction groups such as Honeywell and Halliburton.

MAJOR EQUITAS SETTLEMENTS SINCE 2003