Ministers have come under fire for not offering more support to the sacked Heathrow catering workers.
Gate Gourmet sacked 670 catering workers at Heathrow
Union leaders sought support from delegates at Labour's annual conference in Brighton for lawful secondary action in disputes like that at Gate Gourmet.
A card vote was taken and the result will be announced on Tuesday morning.
The conference did agree to another union demand that the controversial opt out from the Working Time Directive should end.
But Trade and Industry Secretary Alan Johnson made it clear in a keynote speech that the government did not want a return to 1970s style industrial relations.
Some of the sacked Gate Gourmet workers sat in the public gallery to listen to the debate and were given a standing ovation by delegates.
Tony Woodley, general secretary of the Transport and General Workers' Union, said the 670 sacked workers had been treated "shamefully".
And he called on Labour to stand up to the exploitation of low-paid employees.
"It is not about going back to the 1970s, it is about protecting workers' dignity and stopping opportunist bosses victimising ordinary men and women," he said.
He said the Gate Gourmet row had exposed severe weaknesses in employment law, and he was disappointed the government had taken seven weeks to condemn the company's actions.
Mr Woodley said the union was not calling for "wildcat" action and was prepared to make solidarity support in disputes subject to a ballot of workers.
"What is this movement about if it is not solidarity with those least able to defend themselves?" said Mr Woodley to loud applause.
The T&G claimed it had the support of Labour's National Executive Committee for its motion.
But complained that a "shabby manoeuvre" by the party had prevented members taking a vote.
Mr Johnson said unions in the UK enjoyed better rights than their counterparts in other European countries.
The successful motion by Amicus called for a number of European employment directives to be implemented in full, in direct opposition to the stance taken by the government.