Unions have won a Labour conference vote on their call for employment law changes to allow industrial action in support of a strike elsewhere.
The motion was prompted by the Gate Gourmet dispute
The Transport and General Workers' Union's motion, prompted by the dispute at airline catering company Gate Gourmet, was passed by 69% to 31%.
The plan was overwhelmingly backed by unions, who will use the result to press ministers to change the law.
Trade secretary Alan Johnson on Monday ruled out allowing secondary action.
He said during a debate on the issue: "In our quest for full and fulfilling employment, we realised that we could not go through the eighties and nineties only to emerge in the seventies.
"Back then, this party supported secondary action and opposed the minimum wage. Now it's the other way round - and that's how it needs to stay."
Strikes in support of fellow workers have been illegal since 1980.
Recent wildcat action by British Airways' Heathrow baggage handlers in support of sacked staff at Gate Gourmet has led to calls for a change in the law.
The TGWU motion also called for protection against dismissal for workers who go on strike, and the barring of replacement workers being drafted in by companies during disputes.
Labour's constituencies voted against the motion by 60% to 40%, but the motion was passed after 99.6% of unions voted in favour.
TGWU general secretary Tony Woodley said: "This is a tremendous vote and we have had much greater support from the constituencies than we expected.
"It shows the government has lost the argument on solidarity action and on the right way to respond to the Gate Gourmet dispute.
"Ministers will now have to listen and accept that the present state of employment laws is rejected by the overwhelming majority of the Labour Party and the movement."
The director general of the Confederation of British Industry, Sir Digby Jones, told the BBC he thought it would "a regressive step for what is such a successful competitive economy. India would think it was Christmas Day frankly. And we cannot harm the flexibility in our labour market by allowing unions to march the government back towards 1970".