Nick Clegg's Liberal Democrats have vowed to face down "ruthless" and "extreme" forces in the Tory party to protect the British people from right-wing policies that would widen inequality and benefit the rich.

At a rally on Saturday night to open his party's annual conference in Birmingham, Clegg underlined the Lib Dems' newly combative approach to the coalition, describing David Cameron's party as "political enemies" who must be taken on when necessary in the national interest. After a traumatic year during which the Lib Dems' popularity plummeted, a poll has shown that only 47% of those who voted for them last time would do so again. Having been accused of abandoning his party's principles, Clegg struck a markedly more assertive note.

While trumpeting his party's successes so far in influencing health and tax policies, he said it was more prepared than ever to "fight tooth and nail" for what was right. "We are prepared to be awkward," he said. "We are not here to make things easy. We're here to put things right."

In an interview with the Observer, his deputy Simon Hughes goes further, telling the Conservatives they have no mandate to drive through a rightwing agenda. Hughes says the Tories have shown themselves to be "ruthless" operators in the first 16 months of the coalition over the referendum on electoral reform and boundary changes, and says the resurgent right of the party is "extreme" on issues such as Europe and tax.

He says the Tories must come to their senses and realise that they did not win the last election – and that they rely on the Lib Dems for power.

"Not only did they not win but they got a third of those who voted," he said. "The Tory party is not the dominant party in British politics that it used to be. It is absolutely not the dominant force in Scotland and Wales that it used to be. The Tory right have forgotten that."

In a rebuff to Conservative hardliners, he adds: "There is absolutely no majority in parliament for your views. If there is a coalition government in the national interest, then extreme remedies and answers are not appropriate."

The comments are bound to infuriate Conservatives as the conference season opens. Many Tories are beginning to resent profoundly the way the Lib Dems are already watering down Tory changes on health and education and blocking Cameron from developing a more hardline approach on Europe.

Clegg and his ministers are now convinced they can claw back some of their pre-election popularity if they can demonstrate that they are reining in the Conservatives and stamping their own mark on government. Deep division between the coalition partners will surface in Birmingham over tax, welfare, health, pensions and last month's riots. The party leadership will announce it will veto the abolition of the 50p tax rate for people earning over £150,000 – a key Tory right demand – unless other measures, such as a mansion tax, are imposed. It will also unveil plans to exempt the first £12,500 of earnings from tax, raising the target from its current level of £10,000.

Hughes says the party has to make the fight against wage inequality in the private sector a key theme. He said he is pushing hard for measures to limit the gap between the highest and lowest paid staff in the private sector. "The differentials are obscene," he said. "Liberal Democrats have to be clear. If Labour is really relaxed about the stinking rich, some of us are not relaxed about it."

Hughes also insisted that reform of party funding was essential to stop the Conservatives running ruthless campaigns – as they had against electoral reform. "The Tories can be nastier – with a result – if they are allowed to collect more and more money legitimately."

On tax, he said the UK properties of wealthy non-domiciled individuals should be hit. "It would be entirely reasonable to say that if someone is not domiciled in this country but has six mansions they should be paying more into the system." Danny Alexander, the chief secretary to the Treasury, will announce the commitment of £600m to boost infrastructure projects and will attack bankers who fail to lend to businesses. "Our judgments about what needs to be done should be driven by the liberal economy we want to build," he will say.

On Saturday night, the Lib Dem equalities minister, Lynne Featherstone, dismissed suggestions that Cameron had been a major force behind the move to legalise gay marriage when she claimed ownership of the policy. "Conference, this is a Liberal Democrat policy," she said.

Clegg said his party had shown courage entering a coalition that was now shaping policy by "cutting taxes, not for the rich, but for millions of people on low and middle incomes". The Lib Dems could have "bottled" the chance to govern but instead "rose to the challenge", he said, "and we did it knowing it meant working with our political enemies and almost certain short-term unpopularity".

The party leadership was celebrating the failure of former health spokesman Evan Harris to force a vote on the NHS. The Lib Dems believe they are making more progress to dilute the reforms behind the scenes.