Bill Shorten has called on the Morrison government to suspend the controversial robodebt scheme while unveiling a new “David and Goliath” class action to be spearheaded by Gordon Legal.

Shorten was flanked by Gordon Legal senior partner, Peter Gordon, who told journalists in Canberra on Tuesday the proposed action would allege the federal government financially benefited through the robodebt scheme when it wrongfully collected and banked money that legitimately belonged to recipients.

The former Labor leader, now shadow minister for government services, declared the government had dug in behind the scheme despite a continuing outcry about it because “they are hoping they can shake down people into paying up”.

“This is a government building their … position based on this faulty, immoral and quite possibly illegal scheme, but they should suspend it and rule out extending it to anyone else, and in fact they should revisit their own files and perhaps sit down and work out why this is wrong, and stop it.”

Shorten said it was time to test “the legal foundations of robodebt, because my own research in the last couple of months has led me to believe it is almost certainly illegal”.

There is a sickness at the heart of robodebt which needs to be cured Bill Shorten

“I just have to do research through the stories [the media has] covered to say there is a sickness at the heart of robodebt which needs to be cured.”

Separate to the proposed class action, Victoria Legal Aid has brought an action on behalf of Deanna Amato to test the legality of the robodebt scheme. That challenge will go to trial in December. Gordon said the class action would proceed in concert with existing legal proceedings.

Shorten said on Tuesday there had been a pattern from the commonwealth of wiping the debt at the centre of legal challenges, possibly because the government was “scared” to prove the legal basis of the scheme, and that pointed to grounds for legal challenge.

Concerns about the legality of the scheme have been flagged for some time. A former member of the administrative appeals tribunal argued earlier this year the robodebt scheme involved enforcement of “illegal” debts that in some cases are inflated or nonexistent.

That scathing indictment of the program was contained in an academic paper by Terry Carney that also accused Centrelink of failing to defend the legality of debts in the AAT. Carney suggested the tribunal should set aside debts until the agency has proved the amounts are correct.

An ombudsman’s report in 2017 on the rollout of the automated debt recovery service also identified multiple failures that placed unreasonable burdens on welfare recipients and staff.

Gordon said on Tuesday the lived experience of robodebt was the system put debt collectors on to innocent people to chase unlawful debts, and the class action would seek repayments with interest, a wiping of penalties, and damages for distress and lost reputation.

He said using a flawed algorithm to claw back unlawful debts meant the commonwealth had engaged in unjust enrichment in the eyes of the law, and “wronged” a class of people.

Gordon said the class action component of the legal strategy was relatively straightforward, but he said there was an element of innovation because the high court would have to recognise legal principles that “may break new ground”.

“We think there is a strong legal basis and a strong factual basis [to proceed],” Gordon said. He said “a number of people” had already contacted the firm through referrals from legal aid, and it was likely one of those people would be the test case.