“This is an emergency, we will shortly be making an emergency landing on water,” was the message played.

Passengers on board Saturday’s flight from Miami said they feared for their lives when they heard the announcement, saying they should brace themselves for an emergency landing.

Duncan and Tracey Farquharson, from London, told the Daily Telegraph a flight attendant then made an announcement over the intercom, saying the message had been played in error.

Mr Farquharson, 58, an engineer, said they were about three hours into the flight when the automated message was playing. “It still makes me very emotional thinking about it now – it was very traumatic,” he told the Telegraph.

“We looked at each other and figured we were both about to die. Families with children were distraught and people were in tears. It was very distressing.

“About 30 seconds later one of the cabin crew told us to ignore the announcement and accept their apologies but the tone of suggested they had not grasped how seriously we had taken it.”

Mr Farquharson accused the airline of being blasé about the incident, adding: “Imagining yourself plunging towards a cold, watery grave in the middle of the Atlantic is a pretty horrific thought.”

Mrs Farquharson, 51, an administrator, added: “The captain didn’t even say anything about it until when we were coming in to land and even that did not explain what had happened.

“It still makes me very emotional thinking about it now – it was very traumatic.”

A British Airways spokesman said: “The cabin crew cancelled the announcement immediately and sought to reassure customers that the flight was operating normally.

“We would like to apologise to passengers on the flight for causing them undue concern.”