Two men who lived in so-called Mr Fluffy homes have been diagnosed with the asbestos-related cancer, mesothelioma, the ACT Government has confirmed.

ACT Chief Minister Katy Gallagher said it was understood the men lived in properties containing Mr Fluffy loose-fill asbestos for a considerable length of time.

The ACT Health Directorate began investigating after the cases were brought to its attention by the Fluffy Owners and Residents' Action Group.

More than 1,000 houses across Canberra had loose-fill amosite asbestos installed in the roof space by the Mr Fluffy company in the 1960s and 1970s.

A Commonwealth funded clean-up program 20 years later attempted to remove all the potentially deadly fibres.

However remnant fibres have been found in the living areas of at least 10 houses.

The fibres are thought to have been dislodged from wall cavities and sub-floors during renovation work.

Ms Gallagher said the men approached her after a community forum.

She said she could not be sure if there was a direct link between their illness and Mr Fluffy insulation, but it could not be ruled out.

"I had a short discussion with them but I think it's almost impossible to identify," she said.

"At one point they are living in a Mr Fluffy home and they now have mesothelioma.

"But we also know that people can have exposures which might lead to asbestos-related cancer in a range of areas."

Ms Gallagher said the unique situation of Mr Fluffy houses in Canberra made it difficult to predict if there would be more mesothelioma cases in the future.

"This is the only city in the world as I understand it where this kind of asbestos was pumped into people's roofs," she said.

"It was later remediated to a certain degree, so there isn't anywhere where we can mark ourselves against.

"There probably is a very strong case for the funding of research into this population so we can actually learn from it.

"But we also know it's a 30-35 year period from exposure to the onset of illness, so it would have to be long and ongoing research."

Owners paid 'more than $50,000' to demolish the house

Last year, seven cases of mesothelioma were diagnosed in Canberra, which is a similar figure per head of population to the national average.

But ACT Health said being exposed to loose-fill asbestos did not necessarily mean a person would develop asbestos-related medical conditions.

Residents of the 10 properties found to contain remnant fibres were forced to move out after safety checks were carried out earlier this year.

Today the first Mr Fluffy house was demolished in Canberra's south.

The owners of the property in Woden Valley moved out after a safety assessment found loose brown asbestos fibres in living areas.

The owners were not then able to enter the house without protective equipment.

Most of their clothes and soft furnishings had to be destroyed to prevent any tiny asbestos fibres from spreading.

This house has become the first Mr Fluffy property to be destroyed since an adverse asbestos assessment. ( ABC News )

Brianna Heseltine from the Fluffy Owners and Residents' Action Group said families who planned to demolish their homes were facing huge costs and needed urgent assistance.

"They've had to leave behind all of their possessions and move in with relatives," she said.

"They have been out of their home for three months and they've been desperately waiting to rip down the home so that they can reclaim their lives."

Ms Heseltine said the owners had paid more than $50,000 to demolish the house safely.

"When they bought their house, they bought a home, they didn't just buy an empty block of land," she said.

"They've been out of their home, but they can't afford to keep paying the mortgage and having those extra expenses.

"They just need to move on with their lives, and so this is the first home in our group being demolished."

First Mr Fluffy home safely demolished: WorkSafe

Work Safety Commissioner Mark McCabe said the home had been safely demolished this morning.

"We're confident that after today's demolition, that site will now be free of loose-fill asbestos insulation," he said.

"The material will be taken away and appropriately dealt with.

"The site will be completely remediated, that site will be free of asbestos as will any other site that's been treated the same way."

Mr McCabe said he was aware some people were surprised that onlookers and inspectors were not wearing masks near the demolition site.

"It really wasn't required," he said.

"The bulk of the material was taken away weeks ago and the internal surfaces were all sprayed and sealed so that there was really minimal chance of any release of fibres today.

"What few fibres might have been released would've been dispersed into the general atmosphere."

ACT Health has encouraged anyone concerned about their health to see their doctor for an assessment.