The Transport & General Workers Union says all the striking British Airways staff, who were supporting 800 workers sacked from a catering firm, are returning to work.
Several hundred baggage handlers, loaders, cargo staff and other workers at the airport staged the lightning strike in support of employees of caterers Gate Gourmet, which supplies BA.
The firm sacked 800 employees in a row over working practices
The TGWU accused the firm of acting in a "disgraceful" fashion and called on BA to exert pressure to resolve the dispute.
A meeting is underway between the TGWU and Gate Gourmet, with the conciliation service ACAS, to try and break the deadlock.
Meanwhile, British Airways has pledged to rebook or refund all the passengers caught up in the crisis, which is estimated to be costing the company around Ј10m a day.
BA put up about 4,000 passengers in hotels on Thursday night but hundreds more were forced to sleep in the terminals. Nearly 500 flights have had to be cancelled.
No flights are expected to take off or land before 8pm today at the earliest, Sky News reports.