0813 GMT September 18, 2019
BA pilots are due to strike on September 9, 10 and 27, but BA also told customers with tickets booked on other days that their flights were canceled, BBC reported.
The company admitted on Saturday that it had told some passengers to rebook or get a refund by mistake.
BA said it had received nearly 40,000 calls and was working around the clock.
After initially sending one email informing customers of cancelations, BA then sent a second email to some people saying their flights would go ahead as planned.
But in the second email, passengers were not given a link to automatically rebook onto their original flight, meaning they had to contact BA directly.
Some customers say they have spent hours trying to get in touch with BA's customer services without success.
One woman, Josie Simpson, told the BBC she called the airline 67 times to try to rebook a family holiday to Florida.
The company's Twitter feed has also been inundated with messages from frustrated people.
In response to one passenger, BA said, "We're extremely sorry that you're having difficulties trying to rearrange your flights. Our teams have been working tirelessly to help as many of our customers as possible, in these unprecedented circumstances."
Some customers who were told their flights were not scrapped after all have been left confused about whether their decision to accept a refund has now been canceled.
Others have complained that they have been left out of pocket.
Ellie Kormis, from Surrey, spent the whole of Saturday trying to speak to BA after being told one of her flights for her family's package holiday to Greece was canceled.
She said they ended up booking new flights — which extended their holiday by three days — and extra accommodation, costing more than £2,000.
"You're left in a situation where you can't speak to anyone — and you fear you'll either lose your holiday or be left out of pocket," she said.
BA then contacted her by email to say her flight wasn't canceled after all.
She said it was "an epic mess up on their part," joking that she had lost hope she would ever get through to speak to someone at BA.
Laura Gillespie, 48, from Perth, said she accepted a refund and booked new flights and trains after being told her flight from London to Edinburgh had been axed.
But she said BA now say they won't give a refund as the flight has not been canceled.
"I've now got flights booked with two different airlines going to the same place and I'm £140 down. I know it's not a lot of money compared to some folk who have spent thousands but it's so annoying."
The British Airline Pilots Association (BALPA) said on Friday the strikes were a "last resort" born out of "enormous frustration" with airline management.
Pilots have rejected a pay increase worth 11.5 percent over three years, which the airline put forward in July.
BA says it carries 145,000 customers every day — with a fleet of more than 280 aircraft - and a BA plane takes off from somewhere in the world every 90 seconds.