The left engine of the Boeing 777-200 burst into flames at McCarran International Airport, forcing 157 passengers, 10 crew and three pilots to evacuate through emergency slides.
Fire officials said at least 14 people were taken to hospital with minor injuries, mostly caused by them sliding down the inflatable chutes to escape.
The captain was named as Chris Henkey, from Reading, Berkshire, who has over four decades of flying experience with BA.
His ex-wife Marnie, who is a former cabin crew member and with whom he has a daughter, expressed her relief that he and the rest of the crew got out safely.
“He is safe and happy,” she told the Guardian.
“I’ve had some messages from him. He did a bloody good job.”
The airport released a statement which said it was first alerted to the emergency at 4.13pm local time (12.13am Irish time) and within five minutes everyone was off the plane and the blaze was extinguished.
An audio recording which appears to be the conversation between the captain and air traffic control shows how efficiently the emergency was dealt with.
Speaking calmly and clearly, the pilot said: “Mayday, mayday, Speedbird 2276 request fire services.”
The woman in the control tower immediately replied: “Heavy fire services on the way.”
Forty seconds later the captain added: “We are evacuating on the runway. We have a fire. I repeat, we are evacuating.”
According to reports the captain was applauded by passengers when he spoke to them in the safety of the terminal building.
BA would not confirm the identity of the captain but said he was “very experienced and has flown with British Airways for 42 years”.
Aviation expert Julian Bray paid tribute to the way the passengers were guided to safety.
He said: “It was a textbook emergency evacuation under difficult conditions because that smoke was thick, black and acrid.”
The BA flight from Las Vegas was set to depart for the 10-hour flight to Gatwick when the crew noticed the fire and evacuated all on board.
BA issued a statement which said the plane “experienced a technical issue” and the crew “evacuated the aircraft safely”.