The Government is to press ahead with plans to slash an extra £10 billion from the welfare budget by 2016-17, on top of the £18 billion cuts already under way, Chancellor George Osborne will say on Monday.

Mr Osborne has secured the agreement of Work and Pensions Secretary Iain Duncan Smith to the savings, which he said in his March Budget would be necessary in order to avoid additional cuts in other Whitehall departments.

Among the payouts which look set to be targeted is housing benefit for the under-25s, who Prime Minister David Cameron has previously said should live with their parents if they cannot afford to fund their own home.

Mr Duncan Smith is understood to have initially resisted the cuts proposal, arguing that savings should be found by means-testing benefits such as free bus passes and winter fuel payments for wealthy pensioners.

But in a joint article on Monday, he and Mr Osborne said they have reached agreement that the savings can be found without touching the universal benefits for pensioners. "We are both satisfied that this is possible and we will work together to find savings of this scale," they wrote, rejecting the alternative options of cuts to economically-productive spending, higher taxes, or more borrowing and debt.

The announcement, to be spelt out in Mr Osborne's keynote speech to the Conservative Party conference in Birmingham, will set the Tories on collision course with their Liberal Democrat coalition partners.

Deputy Prime Minister Nick Clegg told his own party's conference last month that he would not allow "wild suggestions" of a £10 billion cut in welfare, while Chief Secretary to the Treasury Danny Alexander told delegates: "We simply will not allow the books to be balanced in a way that hits the poorest hardest".

Mr Osborne will say that a further £16 billion of savings must be found in 2015/16 alone to meet his target of balancing the nation's books within five years, and he will make clear that sums of this magnitude cannot be found simply by increasing taxes on the rich.

Both the Chancellor and Prime Minister David Cameron indicated that the rich will be expected to "pay their fair share" towards deficit reduction, but ruled out the introduction of a "wealth tax" such as the mansion tax on expensive properties favoured by the Lib Dems.

In Monday's speech, Mr Osborne will argue that while the Government should not attempt to balance the budget on the backs of the poorest, it is an "economic delusion" to think it can be balanced on the wallets of the richest. It is wrong to have a welfare state where those who live on benefits can be better off than those who have a job, he will argue.