"In anywhere but the craziness of Canberra, presented with the challenge of renovating a 1920s house with important heritage considerations, any rational person would get a shortlist of the top three or four architects who specialise in that field and choose one of them," he writes in his memoir, released on Monday.

"But not in Canberra, where the renovation of the Lodge sums up everything that's wrong with the unworldly culture of the public service," he said.

Mr Turnbull said a new Lodge should be built at the Lake Burley Griffin site set aside for the purpose.

The Lodge renovation was one of the worst he had seen, Mr Turnbull writes.

"It turned out it had been overseen by Peta Credlin, but not even that explains the fiasco. There was no fixed-price contract entered into with the builder, no agreed design, the requirements and plans kept changing, and the architect, as he later told me himself, had limited experience in domestic architecture and had won the job because the Department of Finance esteemed his firm's work on designing the AFP headquarters!"

Ms Credlin said the claim she had overseen the renovation was incorrect. The renovations were initiated under Julia Gillard, and continued under Kevin Rudd and Tony Abbott. "They were not overseen by the PM's office," she said.

"The process was managed by PMC and DOFA not the PMO. We were briefed obviously as things went along but don't forget, Mr Abbott never lived in the property at any time."

Mr Turnbull said the Lodge was not fit for purpose, built in 1926 as a temporary residence and designed "like most posh Melbourne houses of that era, as though it was in England".

"It would be more at home in the stockbroker-belt suburbs outside of London," he said.

Its reception rooms were not big enough for large functions and while it had a beautiful garden, its amenity was rather diminished by Adelaide Avenue, built in 1969 on the site of an old orchard that had been part of the original Lodge grounds.

"Loud traffic noise is ever-present, to the extent that the main 'Menzies bedroom' has to have double-glazed windows so that the occupants can sleep," he wrote.

Mr Turnbull said he would dearly liked to have stayed in the apartment he owned on the Kingston foreshore when he became prime minister but had already copped criticism for not moving into Kirribilli House.

So wife Lucy Turnbull had inspected the renovations and called "in a state of high anxiety", telling her husband that it was a huge scandal.

"It's a complete mess. No planning. They didn't even think of wifi, so there are all these little white boxes lying around the place, and the kitchen is unworkable."

She thought $7 million had been spent.

"I was astonished," Mr Turnbull wrote. "For that kind of money you could have built an entirely new house of that size and had plenty of change left over."

They discovered that more than $11 million had been spent.

Mrs Turnbull paid herself for curtains and upholstery, recruiting Malcolm Fraser's daughter Angela Marshall, who had lived in the Lodge as a child, to help. They had found some of the original furniture in a Canberra warehouse.

One of the few rooms with natural light was on the northeastern corner of the house but a glass-panelled door on the northern side had been bricked up, probably in Malcolm Fraser's day.

"Then in the Credlin renovation the room had been destined to be filled with noisy fridges and office equipment. A complete waste," he writes.

"The door gave me another insight into the parallel universe of Canberra. Once we had determined that there had indeed been a door and that reinstating it would not offend the heritage mafia, the next step was making the door.

"Quite by accident I learned that my department was proposing to spend up to $10,000 on an architect to design the door. Now, all of the doors at The Lodge are the same design. So I pointed out we simply needed a joiner to make a copy of one of the existing doors."

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Mr Turnbull said he had ordered the renovation audit overseen by construction lawyer David O'Donnell, which reported in 2016.

"The conclusions were essentially as I have described - a clueless client who failed to give clear and consistent direction to the various contractors and consultants. Needless to say, the departments of Finance and of the Prime Minister and Cabinet did everything within their power to resist taking responsibility."

The Canberra Times has reported that the upgrades, commissioned under the former Labor government in 2013 had an expected cost of $3.2 million, and originally included asbestos removal, replacement of the degraded slate roof and decaying internal wiring, as well as health and safety improvements.

Former prime minister Tony Abbott approved an expanded scope of works on the advice of bureaucrats, including upgraded security systems, refurbished living areas and bathrooms and replacement of run-down Australian Federal Police guard houses.

Mr Turnbull said if the prime minister was to have an official residence in Canberra, the Attunga Point site should be used for an Australian-designed official residence with public rooms for entertaining and a private apartment suitable for the prime minister.

Kirribilli House should not be used as an official Sydney residence, as it had become under John Howard.

"If there's to be such a place in Sydney, why not one in every other state capital?"

Likewise, there was no need for the governor-general to have a Sydney residence, and both Admiralty House and Kirribilli House should be used as a reception and conference facility.