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Officials at the centre, which monitors radio signals and telephone calls from around the world, have accepted that staff have suffered hearing loss while listening to "enemy emissions".

They blame inadequate headphones which have since been replaced. More than 100 specialist staff at the site in Cheltenham in Gloucestershire have already received cash to fund equipment to help them cope with a wide variety of hearing problems. But that number is expected to rise because of the progressive nature of the illness.

The compensation bill has already exceeded £500,000 in a year, with some employees collecting £20,000. The Sunday Telegraph understands that managers paid out rather than face legal action from staff who claimed that they were being treated unfairly.

The problems resulted from the use of headphones without adequate volume controls. Officials say that the 4,000 workers turned the volume up to full if foreign transmissions were difficult to understand. Some transmissions were accompanied by constant buzzing and crackling. New headphones introduced in 1995 came too late for operators who worked at the centre during the height of the Cold War.

The payouts have been welcomed by the Public and Commercial Services Union, which was established at GCHQ after this Government lifted the ban on unions, although the first claim was made before that. Andy Shepherd, the chairman of PCS, is one of those seeking compensation. He suffers from tinnitus, which is a constant ringing in the ear. "I am one of those who has suffered through excessive use of the headphones.

"I am all right talking to people face to face but I can't hear what people are saying in a crowded environment. I am no good in a nightclub, for instance.

"The payments are important because they help people meet the cost of hearing aids and specialised equipment like teletext televisions."

The agency's decision to offer compensation will have implications for other workers who claim they are suffering because of noise levels at work. The Royal National Institute for the Deaf has warned that as many as 1.3 million British employees may be being subjected to noise levels above 85 decibels.

Last year The Sunday Telegraph revealed how a group of switchboard operators working for British Telecom had been compensated for acoustic shock.