The Unite union is to appeal yesterday's (Monday, May 17) High Court decision that ruled its British Airways cabin crew ballot was illegal.
Union bosses called the judge's decision "an absolute disgrace" after a technicality surrounding spoiled ballot papers made the process unlawful.
Unite boss Tony Woodley said he hoped the Appeal Court would hear their case as early as today.
While the Court's decision came too late for BA to reinstate full services at Heathrow, the airline said 90% of long haul and 60% of short haul were operating.
London City and Gatwick are operating as normal.
Chief executive Willie Walsh last night insisted talks would continue with Unite in spite of the anger caused by the court's ruling.
Unite said it did not blame Walsh for the Court's decision, and insisted it was apoplectic about the way the law has been enforced.
Meanwhile, an industrial relations lawyer has said yesterday's decision will no nothing except delay more strike action and create more uncertainty.
Marc Meryon, who was speaking this morning on the BBC's Today programme, said: "The point is unions have unique privileges which allow them to cause mayhem with strikes without incurring any liability.
"And the price they pay for those privileges in to comply with the detailed ballot and notification rules. Those rules are detailed and they are technical, but they are there for a reason. They are there as much to protect union members, as they are to protect everyone else.
"It would have been very easy for the union to have given all of that information. They union failed to persuade a judge yesterday that they had done.
Meryon said that employers had been looking more closely at the accuracy of ballots as a way of clipping unions' wings.
"The law can't resolve this, all the law can do is delay the inevitable.
"So, in a sense, while British Airways has gained a short-term advantage in having the strikes knocked out, the price they pay is longer term uncertainty because the union can go back and ballot its members all over again and presumably get it right this time and we're back to square one."