The travel plans of hundreds of thousands of British Airways passengers face the threat of disruption next month after pilots at the airline voted to go on strike over pay.

In the ballot, 93% of BA’s 4,000 pilots voted in favour of taking industrial action after rejecting a three-year pay deal. Strike dates have yet to be announced by the pilots’ union Balpa, which must give two weeks’ notice of any action.

BA is now trying to obtain an injunction to prevent a strike, with a hearing due in the high court on Tuesday morning. It means that Balpa could set a strike date for 6 August if the BA injunction attempt is defeated and the union immediately gives notice of planned walkouts on the same day.

The union’s general secretary, Brian Strutton, said the mandate, on a 90% turnout, demonstrated the pilots’ resolve and the need for BA to improve its offer to avert a strike. He said: “Settlement of this dispute is in BA’s hands. We do not wish to inconvenience our customers which is why we have tried to resolve this matter through negotiation starting last November. It is BA who has regrettably chosen to drag this out into the summer months.”

The union claimed the cost to BA to settle the dispute would be significantly less than the financial loss from a single day of strikes.

BA, which carries up to 145,000 passengers per day, said it remained open to peace talks but that its proposed pay offer of 11.5% was fair and had been recommended by the Unite and GMB trade unions to their members working at BA in other roles.

The airline said: “We are very disappointed that Balpa has chosen to threaten the travel plans of thousands of our customers, over the summer holidays, with possible strike action. We continue to pursue every avenue to find a solution to protect our customers’ travel plans and avoid industrial action and we urge Balpa to return to talks as soon as possible.”

Unions have been pushing for a deal at a time when British Airways has reported large profits, bringing in the majority of the €2.9bn (£2.6bn) pre-tax profit recorded by parent company IAG in 2018.

Planned strikes by thousands of airport workers also threaten disruption at Heathrow airport, BA’s main base, this summer.