When a homeowner in Bradfield St, Downer, discovered loose asbestos insulation in his ceiling in 2011, he set off a train of events that led to the $2 million demolition of his house in 2013, and the mass buyback that began at the end of 2014.

The Bradfield St house was missed in the Commonwealth clean-up of homes in the late 1980s. It now appears a second Downer house has come to light, possibly also missed in the clean-up.

No details have been released by taskforce head Andrew Kefford, who said the home was still being tested. He did not confirm a suburb.

"It was identified by people working on the house, they stopped to ask the question, got a single test done. And the testing of a sample of the insulation is very much a yes-no once it's put under the microscope," he said.

On social media on the weekend, the owner of a Downer house said workers had to access the roof after storm damage and noticed the suspicious material then. The assessor said it had the look of failed attempt at a home clean-up at some stage in the past. The house was on no registers.

The six Downer houses on the Mr Fluffy list. Five of the six have been demolished already, with the Bradfield Street house also marked. The address of the latest find has not been released.

Mr Kefford said the discovery of more Mr Fluffy houses was "a small but nevertheless real possibility", and owners of homes built before 1980 should take care.

"In the older houses in Canberra, particularly those built before 1980, we would encourage people to get an asbestos assessment done, not just for the possibility of loose fill but also for the bonded asbestos that's very likely to be present in all of the older houses in Canberra before they start doing work," he said.

To date, six houses have been discovered, missed in the Commonwealth survey and clean up.

Felicity Prideaux, of the Mr Fluffy Full Disclosure Group, renewed her call for a board of inquiry into the Fluffy disaster - a move the Labor government has resisted. The Liberals have pushed for a Fluffy board of inquiry, leaving the power to force an inquiry in the hands of the Greens. But so far, the Greens' Shane Rattenbury has not done so.

"They need to stop the story that they are spreading to the Canberra community that we are ridding Canberra of Mr Fluffy," Ms Prideaux said. "They are obviously not ridding Canberra of Mr Fluffy for a number of reasons."

She cited not only the discovery of new houses, but the commercial premises that still contained the asbestos - with still no action on a building at the Ainslie shops whose ceiling contains Mr Fluffy insulation. And she pointed to the taskforce's decision to leave sheds and other outbuildings on blokes cleared for resale, with Ms Prideaux saying sheds could well be contaminated by items stored under homes and in roof spaces.