The cost of going to the dentist had become so out of reach for a Northern Territory cattle station worker that he travelled to Cambodia to have 30 years of delayed treatment attended to in three days.

Two million Australians avoid or delay going to the dentist each year because they cannot afford it, a new report from the Grattan Institute says.

It makes the case for the gradual introduction of a universal dental scheme with no out-of-pocket expenses.

The report says such a scheme should focus on check-ups and early intervention procedures, and estimates that it could cost the federal government $5.6bn a year.

“When Australians need to see a GP, Medicare picks up all or most of the bill. When they need to see a dentist, Australians are on their own,” the report said.

“There’s no compelling medical, economic, or legal reason to treat the mouth so differently from the rest of the body.”

Robert Roehlen, 56, said such a scheme would be a godsend. He counts himself lucky that he could afford the south-east Asia trip to fix several problems with his teeth.

“Multiple crowns on plates. Many, many teeth pulled. $1,800. Never ever looked back, brilliant work,” he said.

His last dental visit was eight years ago – an emergency tooth removal because of an abcess. Roehlen still has “intermittent low level pain”, but plans to deal with it once it becomes “unbearable”.

“What I really have noticed is so many men, particularly of my generation and background, have horrendous teeth, many with barely none and all the social problems, eating and stigma issues that go with it,” he said.

Roehlen is a bore runner on a station near the township of Kalkarindji [Wave Hill].One of his colleagues has even worse oral health.

“He has nearly no teeth left. Nobody can understand him because his mouth is deformed and he has a hell of a time eating,” Roehlen said.

“Go to any blue-collar working man’s pub and just check out the older guys and girls and it’s painfully obvious something is wrong. You might expect it in third world countries but it shouldn’t be the case here, should it?”

The institute’s report said low-income adults had fewer teeth, on average, than people with higher incomes.

“On average, people with household incomes below $30,000 a year are missing 8.6 teeth, whereas people with household incomes above $140,000 are missing just 3.2 teeth,” it said.

Existing public dental schemes were inadequate, uncoordinated and inequitable across states, the report said.

Poor oral health can be a risk factor for heart disease, stroke and diabetes.

Narelle Everard, who has worked for the Royal District Nursing Service Homeless Persons Program for a decade, has seen first-hand the impact of dental inequality on Victoria’s most vulnerable.

During a stint in the Yarra Ranges north of Melbourne, one homeless man she knew pulled a tooth out with a set of pliers because he couldn’t afford to see a dentist.

“It was desperation,” Everard said.

She said programs for the homeless were having to provide soft food because people could not bite into hard items such as apples.

The waiting list to see a public dentist in Victoria was 20 months; in Tasmania it could be up to three years, she said.