The Prime Minister on Tuesday held firm behind the Coalition's policy for a national, non-binding plebiscite on gay marriage despite plans by two Liberal MPs – Dean Smith and Trent Zimmerman – to bring on a free vote as early as August.

As revealed by Fairfax Media, the duo's plans are well advanced, with legislation being drafted and advocates being consulted. The bill is designed to end the long-running impasse and get the issue off the political agenda before the next election.

But their job was made harder when Mr Turnbull made it clear he would not allow any conscience vote when Parliament returns from the winter break.

"People can raise what they like in the party room. Private members' bills have to be considered by the bills selection committee," he said.

"We do not support a bill relating to gay marriage being brought on until there was a vote of the Australian people. We will not support a vote in the Parliament until there has been a plebiscite. We are not going to change our policy."

Mr Turnbull's stance does not necessarily prevent movement, if enough Coalition MPs are prepared to cross the floor to force a debate. If the bill did come on it would need the support of only a handful of Coalition MPs to pass into law.

The renewed focus on same-sex marriage – sparked by a secret recording of Christopher Pyne boasting to his moderate allies that the change may happen sooner than we think – has set off another bruising factional fight within the government.

Amid the instability, Mr Abbott went on the offensive, delivering a combative speech and updating his website with a new slogan: Make Australia Work Again.

In a major speech to the Institute of Public Affairs, Mr Abbott outlined policies he says the Coalition should adopt to rebuild trust with conservative voters, restore its political fortunes and win the next election.

The former prime minister outlined three energy measures to put downward pressure on power prices: freezing the renewable energy target at 15 per cent; a moratorium on new wind farms; and for the federal government to potentially go it alone and build a new coal-fired power station.

He also called for immigration to be temporarily slashed to dampen house prices and encourage wages growth, and advocated banning all new spending except on defence and infrastructure.

He had a blunt message for people hoping he may quit politics: "I'm in no hurry to leave public life, because we need strong Liberal conservative voices now more than ever."

Mr Abbott warned that the Coalition could win the next election only if it draws up new political battle lines that would give the conservative side of politics something to fight for. In a downbeat assessment of the nation, Mr Abbott said Australia "plainly, is not working as it should" and that "we are letting ourselves down".

He said that for conservatives, "our challenge is to stay the course, to keep the faith and to fight the good fight".

Mr Abbott said all political parties were vulnerable to populism, and bemoaned the fact "the whole political spectrum seems to have moved to the left".

He said the government's school funding deal, which was passed last week and hailed by the Turnbull government as a major political victory, might have simply shifted the goalposts rather than ending the war.

Mr Abbott also wants the government to attempt the "mother of all reforms" – amending section 57 of the constitution to get around Senate gridlock and allow twice-rejected laws to be brought to a joint sitting of the Parliament without a double dissolution.

Despite the latest outbreak of instability, Mr Turnbull said the party room was "very harmonious, very united".