The government has refused to tell a parliamentary hearing how many alleged welfare debts have been identified by a flawed and now abandoned calculation method that is likely to force the commonwealth to refund thousands of welfare recipients.

At a fiery Senate estimates session on Thursday night, Department of Social Services and Services Australia officials cited legal advice in refusing to answer successive questions about the botched scheme, which is now the subject of a class action.

Under questioning from the Greens senator Rachel Siewert, the secretary of the Department of Social Services, Kathryn Campbell, refused to say how many debts had been affected by the flawed “income averaging” method, found to be unlawful in the federal court in November.

The social services minister, Anne Ruston, then lodged a public interest immunity claim, prompting claims from Labor and the Greens of a “cover-up”.

Ruston told the hearing that “disclosure of details of the class identified by Gordon Legal could also enable the approximate quantum of the claim to become known”.

“The commonwealth’s ability to respond to these proceedings may be prejudiced if the applicants or their solicitors are made aware of matters covered by this public interest immunity claim,” she said.

Last month the government filed its defence against the Gordon Legal class action, dismissing Gordon Legal’s claims that it had unjustly enriched itself and arguing that it did not hold a common law duty of care while administering the scheme.

After issuing more than 600,000 debts, the government has since promised to review which debts were calculated by averaging Australian Taxation Office data, rather than using evidence such as payslips to prove a person had underreported their work income and been overpaid by Centrelink. It has also said it will no longer issue debts without these “proof points”, in response to the November court outcome.

The failure to provide details about a process that departmental officials had last year anticipated would be complete by the end of January means welfare recipients remain in the dark about when they might receive refunds or have their debts wiped.

Officials from Services Australia declined to say how long the process would take to identify all debts impacted by “income averaging”. And they appeared to suggest that they would not reveal how many were affected even once the process was complete, if the court case was ongoing.

Asked how many had been identified so far, Services Australia’s Annette Musolino declined to respond, citing the court case.

They would also not say what they would do once all the affected debts were identified, saying only that they were reviewing a range of options.

Siewert said after the hearing this it meant there was “no justice in sight for victims” of the scheme.

The Labor senator Deb O’Neill launched a blistering attack against Campbell, who was the secretary of the Department of Human Services when the scheme was established.

O’Neill accused Campbell of being “ill prepared”, claimed that she was seeking to avoid scrutiny, and repeatedly accused her of being closely involved in the program, which is now in disarray.

“Can I just say at the outset how profoundly disappointing it is to [the] 900,000 who were served debt notices and the estimated hundreds of thousands of people who are waiting on a resolution to this matter that was constructed by their government,” O’Neill said.

O’Neill was later scolded by her Coalition counterparts after she asked officials from Services Australia whether they had confidence in Campbell, who oversees their agency.