About a million BA passengers would be affected over Christmas
A High Court judge is expected to decide later whether to allow British Airways an injunction against a planned 12-day strike by cabin crew.
BA claims staff taking redundancy were wrongly included in the strike ballot.
Mediation service Acas confirmed its involvement in the dispute after talks ended without agreement on Wednesday.
Meanwhile, further strikes by baggage handlers are expected to add further travel disruption over the Christmas period.
Even more travel disruption is now expected over the Christmas period:
Airport baggage handlers and check-in staff at Heathrow and Aberdeen airports are set to hold a series of 48-hour strikes in a row over pay, starting on 22 December
Scotland's biggest airline, Flyglobespan, has gone into administration, cancelling flights and stranding thousands of passengers in mainland Europe.
UK Eurostar drivers and on-board staff are due to strike for 48-hours on 18 and 19 December, and 26 and 27 December. However, the company says it will be able to draft in French and Belgian workers to cover, and that there will be no disruption to its services.
By Martin Shankleman, Employment correspondent, BBC News, High Court
If body language is anything to go by, the BA representatives in the High Court seem more confident about victory than their union opponents.
And privately some union officers seem gloomy about the outcome. "Unions rarely win injunctions," confided one Unite representative.
The case centres on a technicality of election law: whether the union knowingly sent ballot papers to about 800 members who were leaving.
It has never been claimed that those votes would have made a jot of difference to the outcome, given the majority of more than 8,000.
But on a point of law, it might be enough for BA to win.
British Airways argued in the High Court on Wednesday that Unite's strike ballot was invalid, because it included BA staff who were leaving the company and therefore would not be working for it during any strike.
In his opening statement, Bruce Carr QC, representing BA, said that 1,000 staff taking redundancy had been wrongly included in the ballot, calling it a "wholesale and deliberate inclusion".
In response on Thursday, John Hendy QC for Unite said the union had been "assiduous" in its efforts to comply with the law.
The union said it sent members a text message on 23 November (eight days into the voting period) telling them not to vote if they no longer worked for BA.
It read: "If you have left, or are leaving BA good luck and please tell Bassa [the cabin crew branch of Unite] by emailing email@example.com. If you are staying please remember to vote yes."
The court also heard details of spreadsheets containing information about leaving dates for staff, BBC correspondent Daniel Boettcher said.
BA told the court Unite should have known this, and should have been aware that these staff should not have been included.
However, the union's barrister argued that BA knew who was leaving and when, but the union did not, and the employer failed to bring the information to the attention of the union.
A judgement is expected later in the day.
While the case was being heard in central London, efforts to reach an negotiated end to the dispute were continuing.
Acas told the BBC that it was speaking to both sides about taking a more formal role in the discussions.
BA chief executive Willie Walsh and senior union officials are understood to have given separate briefings to Acas chairman Ed Sweeney.
"The union continues to explore every possible avenue to secure a solution to the dispute, " a union official said.
Mr Walsh and Unite's joint leaders, Tony Woodley and Derek Simpson, had talks on Wednesday which were adjourned without agreement.
At the centre of the dispute is BA's decision to reduce cabin crew numbers on many long-haul Heathrow flights.
Unite says that this change amounts to contractual changes for remaining crew, made without consulting the union.
It has also accused BA of introducing a pay freeze, along with plans to recruit new staff on lower pay.
BA disputes this, arguing that crew contracts remain the same, and points out that staff at Gatwick have been operating with the reduced crew numbers for years, with Unite's agreement.
About a million BA passengers are expected to be affected by the strike from 22 December to 2 January, if it goes ahead.
The BA strike in numbers
Cabin crew have voted to strike over job cuts and changes to work conditions. On long-haul flights their number will be cut from 15 to 14.
Cabin crew are also unhappy about a planned two-year pay freeze. BA cabin crew have historically been paid more than staff at newer UK rival airlines.
Nearly 11,000 out of 13,500 BA cabin crew are union members - 9,514 of those agreed to industrial action over the Christmas period.
If the strike lasts 12 days as planned - from 22 December to 2 January - it
will ruin travel plans for up to a million passengers already booked on BA
..and British Airways, which is already experiencing record losses, will be hit hard by industrial action and may struggle to recover.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.