Thousands of holidaymakers face disruption after British Airways pilots confirmed they will strike across three days in September.

Travellers received emails overnight saying flights on 9, 10 and 27 September would be hit by a “large number of delays and cancellations”.

The British Airways customer service lines were jammed on Saturday morning with travellers looking to find alternative arrangements. Others messaged the company on Twitter with their frustrations, some complaining they would miss weddings and honeymoons.

The British Airline Pilots’ Association (Balpa) said the airline had rejected its proposals to settle a long-running pay dispute and that it had “no choice but to call this action”. The union said 93% of members voted in favour of the action after rejecting a pay rise package of 11.5% over three years.

Melanie Parker, whose husband booked her a trip to New York for her 40th birthday and to celebrate their anniversary, said she was frustrated with BA’s lack of customer care. “I work in a customer service environment and this level of customer service is unacceptable.”

She said her husband had been trying to reach the airline all morning but had yet to speak to anyone.

The strikes affect Parker’s return tickets, but she said BA had cancelled both her outgoing and incoming flights and given her a refund. She would have preferred the airline to have found her a different return flight.

“We have booked expensive Broadway theatre tickets for our trip and paid for airport valet parking and a hotel at the airport the night before our flight. We have also booked for our bathroom to be completely refurbished while we are out of the house,” she explained.

Peter Dempsey said his family would have to pay for alternative flights to attend a family wedding in Spain as they were unable to change the date of their return trip.

He said: “We have no option but to completely cancel both legs and rebook or they won’t give a refund.”

He said he and three others were booked on the return journey, on 9 Septembe, adding: “I’d estimate we will be about £200 out of pocket.”

He said they had spent £550 on their flights but to return on easyJet would cost £330, or to rebook with Ryanair roughly £200. Dempsey described the service since the announcement as shocking, adding that the airline “clearly don’t have enough people to handle such a crisis”.

Ryan Skeets, 44, said his partner had been calling the BA helpline every hour since it opened, but had not got through. “If we haven’t been able to get through by the end of the day I would definitely question how much resources BA have put into the situation.”

Skeets is meant to fly to Lanzarote with his partner on 9 September, the day the strike is planned to go ahead. He said the lack of support had made him question whether to book with BA again. “They don’t seem to have a great track record dealing with situations that arise.”

He said that while he respected people’s right to strike, BA had to do more to support their customers.

Other flyers complained about a four-week wait for refunds and said bookings on their flights were still listed for sale online.

British Airways said: “We will do everything we can to get as many people away on their journeys as possible. However, it is likely that many of our customers will not be able to travel and we will be offering refunds and rebookings for passengers on cancelled flights.”

It said flights with BA CityFlyer, Sun-Air and Comair were not affected and it was “exploring options to supplement our fleet by using aircraft and crew from other airlines”.

Alex Cruz, BA’s chief executive, said the pilots had been offered what he described as an “incredible, inflation-busting deal”, which would take a captain’s pay to more than £200,000 a year. He said they had been “very badly served” by their union.

Balpa said: “Over recent years BA pilots have made sacrifice after sacrifice to assist the company such as taking a pay cut, productivity increases, closing the final salary pension scheme, giving up annual leave days, a new rostering system, and reducing flying pay.

“In what is British Airways’ centenary year, this will be the very first time its pilots will go on strike. They do so as a last resort and with enormous frustration at the way the business is now being run.

“Our ballot is valid until January, and more dates may be announced until such time as this matter is resolved.”