BAA bosses are meeting with Unite union leaders to try and come to an agreement which will stop airport workers going on strike.
Holidaymakers going away over the August bank holiday could be affected, if it goes ahead.
The talks follow a vote by Unite members over a 1 per cent pay offer, with more than 70 per cent in favour of industrial action.
Unite said members deserved a bigger pay rise after a wage freeze and changes to pension schemes last year.
The Spanish owners of BAA offered an additional 0.5 per cent but this was conditional on changes to the firm's sickness agreement, said the union.
The row involves more than 6,000 security staff, engineers and firefighters at six airports - Heathrow, Stansted, Southampton, Glasgow, Edinburgh and Aberdeen.
Unite said the airports would close down if strikes went ahead which would hit the travel plans of millions of holidaymakers and other passengers.
The union would have to give seven days notice of any industrial action, so strikes could be held before the end of the school holidays.
BAA said it was looking forward to the meeting at the conciliation services Acas, adding: "We hope that we can quickly conclude an agreement, in the interests of the travelling public, our airlines and our staff, the majority of whom did not vote for a strike."
Meanwhile, thousands of British Airways baggage handlers, check-in workers and other ground staff will start voting today on whether to accept savings and job losses as part of the airline's plans to cut costs.