Australian building regulations will be examined by a Senate committee after the deadly London residential tower fire.

The high-rise inferno has also prompted Australian regulators to contact their UK counterparts conducting the investigations.

At least 58 people died in the Grenfell Tower blaze that may have been fuelled by the same flammable cladding found to be responsible for the Lacrosse apartment tower fire in Melbourne three years ago.

“I have no doubt that unless we make changes to our regulation and supervision of cladding, it’s not a matter of if, but when we might see some terrible fire,” Opposition Leader Bill Shorten said in Canberra on Monday.

Labor senator Chris Ketter, who chairs the Senate economics committee, said he will direct the committee to look at national regulations.

“We see it as being a timely reminder that we as parliamentarians should be doing everything we possibly can to ensure that that never happens,” he said.

After the Lacrosse fire, building regulations were examined in November 2015 but Senator Ketter said he was concerned about the rate of progress.

“This is an example of the Senate again seeking to shine a light on this issue to ensure that this terrible situation doesn’t occur in Australia,” he said.

“There’s always the possibility that things could slip through the cracks here.”

The committee hopes to hold public hearings within the next month, bringing in experts, the building construction board and unions to examine the issue.

Crossbench senator Nick Xenophon supported calls for further review and said there needed to be a national audit of buildings across the country.

“The London tragedy is more than just a wake-up call,” he said in Canberra.

“There are now no excuses for any government at a local, state or federal level not to do everything possible to ensure the safety of the occupants and visitors to those buildings.”

The prime minister will write to premiers and chief ministers seeking their commitment to enforcing building regulations and addressing non-compliance.

Cabinet minister Anthony Sinodinos said the government would seek to expand the Senate inquiry to investigate state and territory regulations.

“We have taken a leadership role in driving a national effort to strengthen regulations and compliance with regulations but more work needs to be done,” he told senators on Monday.