Two Auckland flatmates have failed to convince Work and Income they are not lovers and have been ordered to pay more than $150,000 in compensation.

Karel Modderman had and Shirley Eyre had their pension and welfare entitlements cut after a Ministry of Social Development investigation last year.

MSD concluded after the extensive investigation that they were in a relationship, rather than just flatmates, and had been wrongfully claiming the more generous single person's pension and benefit.

Modderman, 68, and Eyre, 62, appealed the decision, adamant that they were not romantically involved, and their cases were heard individually.

Modderman, a former IT engineer at Fulton Hogan, has now been told by a Benefits Review Committee that MSD's original decision will stand. That gives them little confidence that Eyre's appeal will succeed.

They plan to appeal the decisions to the next stage, a Social Security Appeal Authority.

They are caught up in a complex area of the welfare system which advocates are urging the Government to reform. An open letter was sent to Prime Minister Jacinda Ardern late last year urging her to change the way beneficiaries' relationships are policed.

"All I'm doing is telling the truth," Eyre said. "I am not in a relationship with Karel. He has not financially supported me."

MSD investigators, however, pointed to a trove of documents, transactions and witness statements to say the two flatmates were financially and emotionally interdependent.

The ministry decided against a fraud prosecution. But it ordered Modderman to pay back $8400 in pension payments, and told the couple they must jointly pay back just over $150,000 in wrongfully-claimed benefit payments by Eyre over six years.

"I will never be able to pay that back, God no," Eyre said. "I will be paying it off until I die."

Her benefit was reduced from $448 to $227 following the investigation. She said she could no longer afford her rent and she had been forced to apply for a food grant every week to pay for groceries.

"I am so stressed it is just unbelievable," she said.

A report by the review committee said Modderman and Eyre had been emotionally and financially interdependent since 2013, when they moved into a West Harbour flat together.

Among the investigators' evidence were medical forms in which Modderman had named Eyre as his next of kin and declared she was his partner. He had also made hundreds of payments to her, including the purchase of two plane tickets to Sydney.

Modderman and Eyre argued that they supported each other in times of ill health, and that the transactions were typical for long-term flatmates, but MSD said they showed a significant degree of interdependence.

The investigator's reports show the extent to which officials go to prove whether a relationship is "in the nature of marriage".

They secured statements from anonymous witnesses who testified that they had seen Modderman and Eyre coming out of the same bedroom, with Modderman wearing pyjamas.

They also secured information from New Zealand Customs Service which showed that when the two travelled to Australia, they were processed in the same lane at the airport and sat next to each other on the plane. This was used as further evidence that they were in a relationship.

Some advocacy groups say MSD investigations are too intrusive, and have urged the Government to overhaul what they see as a punitive and insensitive approach to beneficiaries' relationships.

MSD has previously said that it had made changes to improve the way it investigated fraud, including making sure any information-gathering was appropriate.