The British Airline Pilots' Association (Balpa) voted in favour of industrial action on 22 July, after three days of negotiations failed to resolve the dispute.

BA-owner IAG sought an injunction to prevent the strike in the High Court, but it was overturned.

The airline then appealed and the Court of Appeal ruled on Wednesday.

This opens the way for the pilots to name dates for a potential strike, which would likely fall in August - one of the busiest months for holidays.

However, Balpa has not announced any strike dates today. The union says it is required by law to provide BA with 14 days' notice of any proposed strike action.

British Airways said it was "disappointed" that Balpa had "chosen to threaten the holidays of thousands" of customers.

Analysis

Tom Burridge, BBC transport correspondent

If you have a flight booked with British Airways in the coming weeks then you will naturally be concerned. But as things stand you don't need to panic because the pilots union Balpa has not set a date for a strike.

By law the union has to give BA at least two weeks' notice and they can call a strike any time between now and January. After this latest court victory for the pilots, logic dictates that the airline will have to offer some kind of compromise in order to avert a strike.

On a single day in the summer BA flies around 145,000 passengers. A strike would cause significant damage to the reputation and finances of British Airways and its parent group IAG. But BA will be preparing for all eventualities.

Balpa teamed up with other unions Unite and GMB to submit a joint pay claim in November.

Then in July, BA offered pilots a pay increase worth 11.5% over three years, which was accepted by Unite and GMB but rejected by Balpa.

British Airways reported a pre-tax profit of £1.96bn in 2018

BA says the offer is "fair", but Balpa argues its members deserve better as the airline has been making healthy profits.

After the latest court ruling, Balpa general secretary Brian Strutton said: "The Court of Appeal has today rightly dismissed BA's attempt to injunct this industrial action on a technicality.

"BA's attempt to defeat the democratic view of their pilots in court, rather than deal with us across the negotiating table, has sadly wasted huge amounts of time and money that could have been put into finding a peaceful resolution. Now the window for negotiation and compromise is closing fast."

In 2018, BA-owner IAG reported a pre-tax profit of €3bn (£2.8bn), up almost 9.8% on the previous year, and declared a special dividend of €700m.

British Airways contributed £1.96bn to that, up 8.7% from 2017's figures.

Ahead of possible strikes, the airline advised customers to review their contact details on its website or contact their travel agent.

It added it would "pursue every avenue" to find a solution to the dispute.