British Airways has lost its legal attempt to block planned strikes by pilots, which could take place next month and disrupt the travel plans of hundreds of thousands of passengers.

The pilots union, Balpa, can now call strike dates with two weeks’ notice. However. it has said it will not set dates until after further talks with the airline, which intends to take its case to the court of appeal.

The high court on Tuesday dismissed BA’s argument that the strike ballot, whose result was announced on Monday, was invalid. Some 93% of BA’s 4,000 pilots voted to take industrial action after rejecting a three-year pay deal.

Balpa’s general secretary, Brian Strutton, said: “Although legally clear to do so, we have still not set any strike dates to give BA one last chance to commit to negotiating on pilots pay and rewards with us at Acas later this week.”

He added: “The company itself has admitted that even one day of strike action would cost more than what our pilots are asking for, so the ball really is in their court here, to look after their pilots and ensure the hardworking public get to continue their holidays as planned.”

A BA spokesman said the airline remained open to talks, adding: “We are very disappointed with today’s decision. We will continue to pursue every avenue to protect the holidays of thousands of our customers this summer.”

Pilots had sought an above-inflation pay settlement that would also include a profit share scheme, reflecting their argument that they took pay cuts when BA was struggling in the wake of the financial crisis and that they should share in the benefit now that the business has recovered. BA provided the largest share of parent company IAG’s €2.9bn (£2.6bn) pretax profit in 2018.

BA, which carries up to 145,000 passengers a day, said it had made an offer of 11.5% over three years – a figure that Balpa disputes. The airline said a similar pay offer made to other BA staff had been already recommended by the Unite and GMB trade unions to their members.

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Planned strikes by thousands of airport workers could also affect holiday flights and bring disruption to Heathrow airport, BA’s main base, this summer, with a series of walkouts starting on Friday.

The airport’s chief executive, John Holland-Kaye, accused Unite on Tuesday of calling the strikes to “flex its muscles”. He added that Unite had deliberately targeted the first weekend after most state schools have broken up, Heathrow’s busiest period.

He said: “People will see longer queues through security but we are focused on getting as many hardworking families on their way as we can, regardless of this completely unnecessary strike.”