Caterer Gate Gourmet has warned it could collapse if it fails to agree an improved deal with British Airways.
No more than six people can picket Gate Gourmet, a court has ruled
The embattled catering company has threatened to walk away from its UK venture, saying it will be forced into administration if talks with BA fail.
Unions are demanding 670 staff axed by Gate must be reinstated and have warned more strikes could affect BA flights.
Meanwhile, BA has said it will not sign another deal with Gate until the company changes its working practices.
Sources at the Transport & General Workers' union welcomed BA's demands, saying it indicated the airline was putting pressure on Gate Gourmet to reach an agreement in the row.
The dispute broke out 12 days ago when Gate Gourmet sacked 670 staff, triggering a wildcat strike by the caterer's staff.
A day later BA ground staff at Heathrow walked out in sympathy, forcing the airline to shut down operations at the airport - resulting in the loss of £30m as it cancelled 700 flights.
Gate Gourmet has set a deadline of 1700 BST on Tuesday for BA to agree an improved catering deal.
"At the moment, Gate Gourmet is not a viable commercial organisation and so administration has to be a real probability," said director Andy Cook.
He added the firm was losing £25m a year and BA's deal was vital to its survival.
Mr Cook added: "There is no way on this earth that anyone is going to support a business which isn't making money and is in fact losing the amounts of money that we're losing."
If the company does go into administration, the day-to-day running of the business would be taken over by a team of administrators, typically accountants, as they looked for a potential buyer.
If a buyer could not be found, the business could cease trading and be declared bankrupt.
However at a meeting in Southall, London, unions accused the company of using the threat of administration as a means to push the airline into a deal.
T&G general secretary Tony Woodley urged BA not to "cave in" during its talks with Gate Gourmet and give millions of pounds to the firm while so many workers remained sacked.
Mr Woodley also warned he was seriously exploring the possibility of balloting for industrial action among the remaining T&G members employed at Gate Gourmet.
TUC chief Brendan Barber also attended the meeting, telling workers: "The eyes of the trade union movement are on this dispute.
"The TUC gives its full backing to the T&G's efforts to get justice for the dismissed workers."
BA has said it will continue talks with the union and Gate Gourmet ahead of Tuesday's deadline.
Last week the T&G called on the airline to intervene as it is Gate Gourmet's biggest client at Heathrow.
"We're trying as hard as we can, working to come to an agreement with Gate, and urge the unions to continue to talk [with the caterer]," a BA spokeswoman said.
"The union was very firm to repudiate the unofficial walkout by [BA] staff, which is important to remember."
BA strongly denied suggestions that it might be interested in buying Gate's UK operations, should the caterer chose to put them into administration.