British Airways (BA) has apologised to passengers who were caught up in the ordeal which began on Tuesday last week.
The flight time from London to Athens is less than four hours, but this journey lasted eight times longer.
A faulty cockpit warning light caused the first flight, due to depart at 1.15pm, to be cancelled at Heathrow.
But that was just the first in a long line of problems for passengers.
The second plane couldn’t take off at its scheduled time of 5pm because cabin crew had exceeded their working hours.
Passenger Geoff Lye said the pilot told them it was “the most embarrassing PA announcement” he had made.
GETTYBritish Airways: A flight from London Heathrow to Athens took 33 hours instead of four
Passengers behind me said they could see flames kicking out from the engine
British Airways passenger
After an hour on the plane due to “security issues”, passengers were allowed to disembark.
BA gave them vouchers for a night’s stay in London, before the travellers returned the next day to board another plane.
This flight did depart at 1.40pm, but just moments later the starboard engine caught fire.
Mr Lye told the Evening Standard: “We just took off and there was a bang and it was the engine next to me. There was this huge noise and a judder, and then there were about six more bangs. It was one bang after another.
“I’m an atheist but even I was praying. Our hearts were racing. Passengers behind me said they could see flames kicking out from the engine.”
GETTYBritish Airways apologised to passengers over the four-plane flight journey
The pilots shut down the right engine and turned back to Heathrow.
Later that night at 7.40pm on Wednesday, the fourth and final plane took off bound for its destination.
Passengers finally arrived in Athens early Thursday morning.
Mr Lye, a pensioner, said he had been loyally flying BA for nearly 40 years but will now avoid the airline.
He added: “There was no communication and it was unbelievable they could get so much wrong.”
BA confirmed there were four planes involved in the two-day ordeal.
GETTYBritish Airways passengers arrived in Athens on Thursday morning instead of Tuesday night
A spokesperson said: “Following a technical fault with the aircraft a replacement was provided, but after crew members went over their allocated working hours, the flight was nightstopped.
“The next day the replacement aircraft returned to Heathrow after a technical fault and another aircraft continued the journey to Athens.
“Our teams on the ground were trying their best to provide customers with as much info as possible when they had it.
We fully appreciate how frustrating this experience has been, and have apologised to our customers for the long delay to their flight.”