Nick Clegg has vowed to play hardball with David Cameron over wealth taxes and Trident as he admitted that the Liberal Democrats had made mistakes during their first two years in coalition.

Kicking off the party's autumn conference, the Deputy Prime Minister conceded errors had been made which would leave "scars" for a long time to come. But he urged activists not to give in to squabbling and retreat to their "comfort zone", insisting LibDem ministers are helping to making Britain fairer.

The rallying call came as Clegg struggled to quell rumblings about his leadership, fuelled by consistently dire opinion poll ratings.

He told the gathering in Brighton there had been "some real highs and more than a few lows" since May 2010, listing crowd-pleasing achievements such as raising the tax threshold towards £10,000, increasing the state pension, and introducing the pupil premium.

He also highlighted areas where the party had blocked Conservative policies, including stopping the Trident replacement being approved in this parliament.

He announced Danny Alexander, Chief Secretary to the Treasury, will take charge of a Whitehall review of alternatives to Trident.

"Danny has spoken out repeatedly about how expensive and unnecessary a like-for-like replacement would be," Clegg said. "There is no-one better when it comes to getting value for money for the taxpayer. I am more determined than ever to find the right alternative to such a monumentally expensive replacement for a Cold War deterrent."

Clegg stressed it is only "half-time" in the Coalition's term of office, and promised to fight for the party's values up to the General Election in 2015.

"One of the most important ways we can do that is by making taxes fairer," he said. "Lower taxes on work and more on unearned wealth. I want to reward people who put in a proper shift, not those who sit on a fortune. People for whom a bonus means a few extra quid at Christmas, not a million-pound windfall."

Aides said Clegg would insist on new taxes for the wealthy – such as the party's favoured levy on mansions – as the price for accepting billions of pounds of extra spending cuts when the coalition sets budgets for 2015-16.

Acknowledging activists' frustration over student tuition fee hikes, the AV referendum defeat and the collapse of Lords reform plans, Clegg said: "There were times in the first half (of the Parliament) when we as a party made errors. And we've learned some hard lessons. When the second half is over we will emerge with a few scars. But we will be able to tell people the things we have achieved. Whether it is in school, in work or in retirement, we are showing people we are a party that shares their values: fairness; openness; compassion; equality; community; diversity."

He delivered a stark warning that failure to maintain discipline and make a success of the coalition would spell disaster for the LibDems.

"This is the first time anyone in modern Britain has experienced a national coalition government," Clegg said. "We must show them it is a form of government that works well for them."

"But we need discipline. We are different from our coalition partners. But if all people see is squabbling then they will think coalition is a messy, incoherent thing. We must not put the progress we have made in jeopardy by retreating to our comfort zone."

Clegg also lashed out at Conservative backbenchers who were seeking to push the Government towards a "turbocharged right-wing agenda" before turning his fire on Labour.

He also rejected mockery of the apology he made earlier this week for the student fees manifesto pledge.

"How about a personal apology from you, Ed Balls, for nearly bankrupting the country after you went on a prawn cocktail charm offensive in the City of London to let the banks off the hook?" he said. "And how about, Ed Miliband, an apology, on behalf of your party, for dragging our country into an unjust and illegal war in Iraq?"