A couple whose calls to triple-0 to report a fire were not answered during Friday's national outage — prompting a mad dash to the nearest fire station — have received an apology from Telstra CEO Andy Penn.

Mary Ann Gongon was forced to jump in her car and drive to the nearest fire station after an electric blanket in her Redfern home caught fire on Friday morning, according to a report by News Corp.

Ms Gongon's husband Apollo Karanges reportedly suffered burns to 40 per cent of his body when he attempted to put the fire out after her calls to emergency services did not connect.

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The Government has confirmed it will conduct an investigation into Telstra's triple-0 outage on Friday, which saw emergency calls from NSW, Victoria, Queensland, South Australia, Western Australia and Tasmania go unanswered after a suspected lightning strike damaged a cable near Orange.

A Telstra spokesman said CEO Andy Penn had personally apologised to Ms Gongon and an offer had been made to help with temporary accommodation.

"This sadly demonstrates that even one missed call through triple-0 is one call too many," the spokesman said.

"Any impact to people or property as a result of the situation is extremely concerning.

"We take our responsibilities to connect people to triple-0 very seriously and have deeply apologised for the impact to services."

Telstra said significant fire damage to earth around the damaged cable was consistent with lightning, but a full investigation would examine the cause of the fire.

Initial investigations showed that a "key piece of equipment did not respond as intended" which resulted in the failure of calls to be re-routed, the spokesman said.

Car crash victims unable to get through to triple-0

Victorian man Adam Dobie told ABC News his wife had a car accident in Hawthorn on Saturday at 6am and was not able to reach triple-0.

"My wife called triple-0 twice and couldn't get through," Mr Dobie said.

Telstra customers could not reach triple-0 following a small car accident in Hawthorn this weekend. ( Supplied: Adam Dobie )

He said a bystander who rushed to her aid was a Telstra customer and could not get through to triple-0.

"My wife called me and I was only a few minutes away at home. I rushed to the accident and checked she was okay.

"[The] car wasn't going to ignite and checked [if the] other driver was okay."

Mr Dobie, a Telstra user, said he got through to triple-0 about half an hour after his wife's initial call.

He said it was fortunate the accident was not of a serious nature.

"[I'm] just disappointed with a company I have been with for years who are meant to have the most coverage."