As passengers began to panic, a flight attendant apologised over the intercom and said the message was played by mistake.
"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 [it] suggested they had not grasped how seriously we had taken it.
"Imagining yourself plunging towards a cold, watery grave in the middle of the Atlantic is a pretty horrific thought but they seemed very blase about it."
A British Airways spokesman said that the cabin crew immediately apologised and spoke to passengers individually to reassure them.
The airline confirmed that the pre-recorded emergency announcement was activated in error.
The spokesman said, "The cabin crew cancelled the announcement immediately and sought to reassure customers that the flight was operating normally."