Peter Gordon from Gordon Legal and Bill Shorten, Labor's spokesman on government services, announced the case at Parliament House on Tuesday, with Mr Shorten likening the action to David and Goliath.

The case targets the government's online compliance intervention system, colloquially called "robodebt," which uses an algorithm to match a person's income as declared to Centrelink each fortnight to their annual earnings reported to the tax office. The averaging system has resulted in a system raising debts against people with little ability to challenge the system.

Hundreds of thousands of people have received letters asking them to account for their earnings from years before, with the Department of Human Services putting the onus on the welfare recipient to prove a debt doesn't exist.

"Since becoming Labor's spokesman on government services and Centrelink I've become increasingly alarmed and concerned that the toxic robodebt scheme is not just immoral, but it is almost certainly illegal," Mr Shorten said.

The Melbourne law firm will argue the Commonwealth must repay debts collected and provide compensation to people affected by the scheme, basing the case around the idea of "unjust enrichment," that the government has improperly tried to take the money.

"The Commonwealth has used a single, inadequate piece of data, the robodebt algorithm, and used it to seize money and penalise hundreds of thousands of people," senior partner Peter Gordon said. "We'll allege that to simply collect money from hundreds of thousands of people by the simplistic application of an imperfect computer algorithm is wrong."

Mr Gordon said up to 160,000 people could be included in the class action, but that while he expected the case to be "expeditious" it could take up to two years.

Administration law expert and long-time follower of the robodebt issue Darren O'Donavan said the case had a long way to run, and would draw heavily on the result of two cases already being taken to the courts by Victorian Legal Aid.

"They really are at the first step of a very long process," he said.

"What it offers is a systemic remedy if the point of public law is established."

Minister for Government Services Stuart Robert downplayed the case, calling it a political stunt and repeating claims the robodebt system was started by Labor in 2011.

It's not the first time the scheme has been accused of being unlawful, with former AAT member Terry Carney saying it had no legal foundation.