Malcolm Turnbull is having an “identity crisis” and showed an “appalling lack of judgement” when he inflamed the tug-of-war between the left and right of the Liberal Party, critics have claimed.

The Prime Minister said the government was in the “sensible centre” and was not conservative in a speech to a London think-tank, widely read as a takedown of his predecessor, Tony Abbott.

Opposition Leader Bill Shorten jumped at the opportunity to accuse Mr Turnbull of being distracted from governing.

“The Turnbull government is in the middle of an identity crisis and they’ve forgotten what their real job is,” the Labor leader told reporters on Tuesday.

“Mr Turnbull is having an identity crisis. He’s debating whether he’s a liberal or a conservative. But what is beyond doubt, is that he’s not a leader.

“Actually it’s getting pretty serious, the division between Mr Turnbull and the right wing of his party.”

Mr Shorten said either the prime minister or Mr Abbott should leave government “for the good of the nation”.

Jeff Kennett, the former Victorian Liberal Premier, said Mr Turnbull showed an “appalling lack of political judgement” in handling the “incessant brawling” within the party.

.@billshortenmp says @TurnbullMalcolm is having an ‘identity crisis’ on whether he is a Liberal or a conservative https://t.co/VtQFVGDbXi pic.twitter.com/VuwrcIYlvK

— Sky News Australia (@SkyNewsAust) July 11, 2017

“Why would you do it? Why would you do it from overseas? Why would you throw a can of petrol onto a fire?” Mr Kennett told ABC Radio in Melbourne.

“Malcolm has chosen to have a brawl with his own from overseas.

“The leader of the party should have the capacity to be able to bring the party together – be it by strength of personality or through policy.

“On both grounds I think to date sadly Malcolm has failed.”

Mr Turnbull told the Policy Exchange think tank that Sir Robert Menzies deliberately called his centre-right party Liberal, rather than conservative, when he founded it in 1944.

“The sensible centre, to borrow the phrase from my predecessor Tony Abbott, was the place to be. It remains the place to be,” he said.

The Australian and British PMs visited the Borough Markets before meeting to discuss trade and terrorism in London. Photo: Getty

Cabinet moderates have backed the prime minister’s comments.

Foreign Minister Julie Bishop and Minister for Defence Christopher Pyne both said Mr Turnbull was merely outlining the party’s values and traditions.

Environment Minister Josh Frydenberg and conservative Eric Abetz also stood by Mr Turnbull.

Nick Greiner, the new Liberal Party Federal President and former NSW Premier, said Mr Abbott’s plan for the government was “never going to happen”.

He said the “sensible centre” won elections.

Senator Cory Bernardi, who broke ranks from the Liberal Party to form Australian Conservatives, said the comments reinforced the need for his splinter party.

Pauline Hanson took Mr Turnbull’s comments to mean One Nation was “officially Australia’s largest conservative party”.

“The stitching is clearly coming undone in the coalition,” her chief of staff James Ashby told The New Daily.