The Shrewsbury 24 Campaign reverted to a paper petition after claiming its e-petition was failing to register everyone signing it.
The e-petition attracted 37,000 names, while the paper version has now been signed by 70,000 people in towns and cities across the country as well as at union and other conferences.
The petition will be handed in to 10 Downing Street by union leaders and Royle Family actor Ricky Tomlinson, one of the 24.
The pickets were arrested five months after the 1972 building workers' strike and charged under the 1875 Conspiracy Act, with six sent to prison, including Tomlinson. The campaign group wants all documents relating to the case to be released, claiming they would prove that a "massive miscarriage of justice" was handed out.
Eileen Turnbull, the group's researcher, said: "We are delighted with the progress we are making and we are convinced that the unjust convictions will be overturned."
Steve Murphy, general secretary of construction union Ucatt, said: "Parliament now has a moral duty to debate the case and the Government must come clean and publish all the papers relating to the pickets' case."
Rail Maritime and Transport union leader Bob Crow said: "It is clear that there was a conspiracy at the highest level in 1972 to blacklist and fit up trade union activists and it is time for all the papers to be released and for those that were wrongly imprisoned to be given justice at last."