Unions and management held crisis talks with a conciliation service on Monday in an attempt to prevent a strike which could shut down six British airports on a key holiday weekend.
Members of the Unite union, including firefighters and security staff, voted by three to one to take action over pay.
There are fears that the union will target the three-day August 28-30 holiday weekend, one of the busiest periods of the year for air travel.
Any action would affect not only London Heathrow -- the world's busiest international passenger airport -- but also London Stansted and Southampton in England, and Edinburgh, Glasgow and Aberdeen in Scotland.
Unite and the airports' owner-operators BAA accepted an invitation from conciliation service Acas to sit down for talks, while union officials are due to meet shop stewards later Monday to discuss strike tactics.
No strike dates have yet been announced.
The union, whose members agreed to a pay freeze last year, has described BAA's pay offer of up to 1.5 percent as "measly".
Unite joint leader Tony Woodley, insisted it was not the union's intention to target the public holiday weekend.
"It is a very busy bank holiday weekend, the last thing genuinely we want to do is to have a disruption on our hands.
"That's why I'm very pleased we're at Acas on Monday talking again with the company and the company will hopefully see a little bit of sense," he told Sky News television.
Woodley added: "There's no reason why a new offer can't be on the table and there's no reason why we can't then re-ballot our people as to what they think about it.
"That's our intention. I don't think our people are greedy. I think they are trying to maintain, from a company who can afford it, just a decent settlement to a traditional wage rise. No more, no less."
He said he had "absolutely no doubt" that BAA would make an improved pay offer.
Only around half of the 6,000 workers balloted by Unite voted, but almost 75 percent who did cast their votes opted for strike action.
BAA said: "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."
A fresh strike would be the latest disruption in a troubled year for air travellers.
European airspace was shut by the Icelandic ash-cloud crisis earlier this year and British Airways services have been hit by a series of cabin crew strikes.