A controversial government crackdown on parenting payment recipients that has forced thousands to get a witness to verify their relationship status has failed to find substantial numbers of people flouting the rules.

The plan, labelled “intrusive, offensive and demeaning” by critics, was to review the relationship statuses of people claiming the single parent rate of payments and was slated to save the budget $93.7m over five years.

At the time, the government insisted 7,400 recipients would have their payments reduced and another 7,400 would be have their income support cancelled. Overall, it estimated that 4% of the 370,000 single parents were flouting the rules.

Figures provided to a Senate estimates committee, however, reveal the policy is falling well short of those estimates and is also therefore seems likely to fall short of the projected savings.

In response to questions from the Greens senator Rachel Siewert, Services Australia said it had finalised 75,598 reviews between 1 January 2018 and 1 November 2019. Only 950 people (or 1.3%) of those subjected to a review were found to be partnered.

Services Australia said it would continue the policy but would not say how much the policy had cost or recouped.

Single people who receive parenting payment get $138 a week more than those who are in a couple, while the difference for Newstart recipients is about $50 a week.

People claiming single parent benefits are required to ask a third-party, who cannot be a family member, to provide a statement on the welfare recipient’s relationship status.

The Australian Council of Social Service chief executive, Cassandra Goldie, said the requirements painted “single parents, the vast majority of whom are women, as untrustworthy”.

“These data show this could not be any further from the truth, with 99% correctly reporting their relationship status,” Goldie said.

“The government is wasting precious administrative resources on relationship status declarations. Considering people wait weeks to have their critical income support payment claims handled, the last thing the government should be doing is tying up Centrelink staff with unnecessary relationship verification claims.”

Terese Edwards, the chief executive of the National Council of Single Mothers and Their Children, said the system was a “very antiquated way” of determining people’s relationship status.

“I think it’s a waste of money, especially with the increase of poverty in single parent families,” she said.

Siewert said: “Once again we see that the government has been unfairly picking on single parents, with the so called verification of relationship status process only showing a small number of people that have not been accurately reporting.

“This is an intrusive process for single parents when they are trying their hardest to support their kids.”

A Services Australia spokesman said the department would continue to conduct the reviews until 2021.

Asked how much the policy had cost and how much it had recouped, the spokesman said: “As this measure was announced under the ‘Better targeting of assistance to support jobseekers’ package in the 2017/18 budget, individual costs are not available.”

“Third-party verification reviews aim to ensure single parents receive the right payment at the right time,” he said. “Under the review process, the department contacts single parents with dependent children, who are in receipt of parenting payment or Newstart allowance, to confirm their relationship status.

“Parents are asked to complete a form with a third party referee and return to the department within 28 days. Parents are able to request an extension, where required.

“If a customer is found to be partnered following a review, they may change to a different, more suitable payment, if they are eligible.”

But Edwards argued that while two people may be in a relationship, that did not mean that they shared financial responsibility for children. She said it forced parents, mostly women, to involve another person in their own personal lives.

The figures come as social security experts raise renewed concerns about Centrelink’s processes for identifying couples following research that claimed the agency sometimes struggles to differentiate between genuine relationships and cases of domestic violence.

In October, the government revealed it had scrapped a policy to conduct 90,000 disability support pension reviews over three years because it far fewer people had been found ineligible than originally expected.