Union members at six airports owned by BAA have voted three to one in favour of striking in a dispute over pay, their union says.
BAA said Heathrow, Stansted, Glasgow, Southampton, Edinburgh and Aberdeen airports would have to close if strikes went ahead, as key staff including firefighters were due to take part.
It said the 50% turnout meant the union did not have a clear mandate to act.
Strike dates are expected to be announced next week.
BAA said: "We regret the uncertainty this vote has already caused our passengers and airline customers.
"Fewer than half of those people eligible to vote have done so and we do not believe this result provides a clear mandate for strike action."
The Unite union, which is fighting a "measly" 1% pay offer, said 74.1% of the 3,054 staff who voted had said yes to strike action. A total of 6,185 staff were balloted.
In addition to the firefighters, the vote was also put to security officers, engineers and workers in various support roles.
Earlier, the much smaller Prospect union, which represents about 100 managerial and technical staff, said its members had also voted in favour of industrial action.
Both sides said they hoped to be able to avert the action through negotiation.
The union said it would be meeting on Monday to discuss a plan, leaving the weekend open for talks.
It would have to give a minimum of a week's notice for strike action, meaning walk-outs could begin from the week starting 23 August.
Some analysts suggest Unite may target the August Bank Holiday weekend that starts on 28 August, but its leaders refused to confirm that.
Unite's Brendan Gold said it was not their intention to ruin people's summer holidays.
"The advice we would give to passengers is to put pressure on the company to come to reach a negotiated settlement," he told a news conference.
Tom Hall, from travel guide publishers Lonely Planet, said travel companies would be putting in place contingency plans when they know the strike dates, such as flying from alternative airports.
"But for Heathrow - one of the world's biggest airports - there wouldn't be the capacity [at other airports]," he warned, meaning some flights would have to be cancelled.