Legal action has been launched on behalf of 10 of the 75 passengers on board the flight from Heathrow to Oslo.
The incident which was triggered by the cowl doors flying off the engines within minutes of the British Airways plane departing for Oslo.
Witnesses reported a plane flying over central London with one engine ablaze.
The lawsuit alleges the 10 passengers suffered serious physical and psychological injuries as a result of the emergency landing which will result in lost earnings, medical bills, pain, suffering, emotional distress and “loss of enjoyment of life.”
Insurers are understood have set aside $25 million ((£16.49 million) to settle the claim for the distress suffered by the passengers on board the stricken flight as well as damage to the plane itself.
One of the passenger clients of the group, Alexandra Townsley, 27, a London solicitor, said: “It was absolutely terrifying; my sister and I had a clear view of the engine fire. I remember thinking to myself that
“I was going to die. I am angry to now discover that this had occurred so many times before and the airlines and manufacturers do not appear to have done anything about it.
“It was horrible, I was right next to the engine when it caught alight. It was bad enough when I saw the cowl fly off and hit the side of the plane.
“I was flying with my younger sister and trying to comfort here. We could see liquid and vapour streaming from the engine before it set alight as we landed.”
An initial report by the Air Accidents Investigation Branch found that British Airways maintenance staff failed to close the engine doors after a routine inspection of the Airbus A319.
But a lawsuit filed on behalf of the passengers in Chicago has blamed Airbus and International Aero Engines, the engine manufacturer, for a long-standing design fault which contributed to the cowl doors flying open during the early stages of the flight.
There are 126 Airbuses with these engines currently in service.
According to the writ, Airbus and was negligent in its design, manufacture, inspection and sale of the aircraft which was sold with cowl doors which could not be easily latched.
The company was also negligent, it is alleged, in failing to adequately warn of the defective doors despite having knowledge of 32 previous incidents in which which the cowl doors had become detached.
The emergency at the start of the late May Bank Holiday weekend led to 193 flights being cancelled creating havoc for tens of thousands of passengers.
An Airbus spokesman said the company would not comment on any litigation matters. A spokesman for the engine manufacturers was unavailable for comment.
A spokesman for International Aero Engines said the company was co-operating with the investigation. “The V2500 engine family has a strong safety and reliability record, and the fleet has accumulated more than 115 million flight hours since entering service in 1989. IAE does not provide information on pending litigation.”