Passengers were forced to leave the plane by the emergency slides on to the runway after arriving at Valencia Airport on Monday evening.
The scene on board was described by one traveller, Lucy Brown, as “like a horror film”.
“Terrifying experience on flight to Valencia,” tweeted Ms Brown. ”Flight filled with smoke and had to be emergency evacuated. Thankfully everyone safe.”
Gayle Fitzpatrick, from Glasgow, Scotland, who was on holiday with her husband Stephen, said passengers were crying and hyperventilating as a result of the incident.
She said: “It was very scary. The flight was just ending, and with 10 minutes to go the flight started descending rapidly as smoke started to fill the cabin. It was horrible white acrid smoke.
“A detector was going off saying the cabin was filling with smoke. There was talk it was an air conditioning unit.
“There were no communications from the crew, some of which started to wear full oxygen masks and protective fire wear.
“Eventually they managed to open the emergency doors and told us to go down the chutes.
“There were fire engines waiting and then we were all ushered into a bus then to the airport.”
Ms Fitzpatrick said the passengers were not told it was an emergency until the plane landed and they opened the cabin doors for the evacuation..
Three people have been treated for smoke inhalation and another 12 were treated for minor injuries they received when they slid down inflatable emergency slides, according to local government officials in Valencia.
Emergency services said they received an alert that one of the plane’s engines had caught fire.
Several passengers complained at a lack of information from cabin crew and airport staff. Others said they were left waiting for more than two hours before being told they could go and collect their belongings from the aircraft.
Stephen McConnon said: “Shocking handling of the emergency scenario at Valencia. Plane full of smoke, no oxygen, no announcements on the plane and no staff dealing with anything in the airport.
“The most terrifying experience of my life and no reaction from you. Shocking!!”
A spokesman for the airline said on Monday evening: “We can confirm that British Airways flight BA422 from Heathrow to Valencia has been involved in an incident today.
“The aircraft, an A321, has landed and all customers and crew have disembarked.
“British Airways teams are assisting customers who are in the airport terminal.”
Additional reporting by Press Association