The owner of a heritage-listed Hobart property containing asbestos will feel the "full force" of the council, the Lord Mayor says, after the home was demolished without a permit and even after locals and a council representative tried to intervene.

The council was alerted after local residents witnessed workers arrive and set to cutting down trees and demolishing the 1890s-era house on Sunday.

Hobart City Council is investigating the presence of asbestos. ( ABC News: Pete Harmsen )

Despite a council representative attending and calling for work at the address to stop on Sunday, operations continued.

Yesterday, council confirmed asbestos was present at the site.

"Not only did the owner carry out this work without obtaining any approvals, he disregarded the cease work direction of a council officer," Lord Mayor Sue Hickey said.

"We have to have these strong rules. It'll be up to the court to decide what happens. But we need this to deter other people doing such stupid and foolish acts and endangering their neighbours."

Ald Hickey said she wanted to see a hefty penalty and believed all her colleagues would want council to "throw the full force of anything we can against this developer".

The owner is facing a possible 10-year ban on any development on the property, Ald Hickey said.

The house, on a 1,406-square-metre block looking out over Hobart's Derwent River, was heritage listed under the city's planning scheme and sold at auction late last year for $445,000.

The council notice requires the owner to:

Immediately stop work

Immediately stop work Engage a licensed asbestos removalist

Engage a licensed asbestos removalist Erect signage restricting access to the site

Erect signage restricting access to the site Prevent material or debris escaping "on to or into" the road or neighbouring properties

Prevent material or debris escaping "on to or into" the road or neighbouring properties Remove all asbestos within three days

Remove all asbestos within three days Provide certification that all asbestos has been removed from the property and the property "is safe"

The 3-bedroom, 1-bathroom house sold for $445,000 in 2016. ( Supplied: realestate.com.au )

Mount Stuart resident Ian Macdonald said he and other neighbours of the property watched on as a group of men arrived and began cutting down trees on Sunday.

"[They] came with chainsaws and started cutting down the 160-year-old Irish yew and this massive bay tree that was here, both of which had preservation orders in place," he said.

"I rang the council at that stage."

A few hours later, residents said, the men turned their attention to the house.

"The guy just got his excavator off the truck and just started smashing the house to pieces," Mr Macdonald said. "He wasn't doing it in any sort of a controlled manner."