Chancellor George Osborne is to vow to "finish the job we have started" in eliminating Britain's national deficit, as he confirms plans to slash a further £10 billion from the bill for welfare.

The benefit reductions come on top of £18 billion cuts in welfare already under way, and are likely to put the Tories on collision course with their Liberal Democrat coalition partners.

But Mr Osborne will say in his keynote address to the Conservative conference in Birmingham that, while the wealthy should contribute the most to the cost of reducing the state deficit, it is not possible to balance the books "on the wallets of the rich" alone.

Mr Osborne is expected to admit that the job of repairing the British economy following the financial crash is "taking longer than we hoped, because the damage was greater than we feared". But he will add: "The economy is healing... Let the message from this conference be clear: we will finish the job we have started."

Among those likely to lose out from the proposed welfare cuts are under-25s, who look set to be stripped of the right to housing benefit in a move which could save the Treasury up to £1.8 billion.

Work and Pensions Secretary Iain Duncan Smith is thought to have resisted the proposals - first floated in Mr Osborne's March Budget - to slice £10 billion from the welfare budget by 2016/17 in order to protect spending in other Whitehall departments. He is understood to have argued that Prime Minister David Cameron should reverse a pre-election pledge to protect universal benefits for older people, such as free bus passes and winter fuel payments, by removing them from wealthy pensioners. But he and the Chancellor announced in a joint newspaper article that they had reached agreement that the savings can be found without touching the universal benefits for pensioners.

The move is likely to infuriate Liberal Democrats. Deputy Prime Minister Nick Clegg told his 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."

But Mr Osborne will say 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. He is expected to say: "Just as we should never balance the budget on the backs of the poor; so it's an economic delusion to think you can balance it only on the wallets of the rich."

Mr Osborne said the planned cap on benefits due to come in next year would mean claimants faced the same choices about how many children to have as working families. The Chancellor told BBC Breakfast: "We are very clear by introducing a benefit cap, for example, next year that there should be a limit on the total amount that you get no matter how many people there are in your family so that no one out of work gets more than the average family gets by going out to work."

Mr Osborne did not deny claims, made in the Financial Times, that austerity measures are set to continue until 2018. According to the newspaper, the Office for Budget Responsibility will report in the autumn that another hole in public finances will need to be plugged. Asked about the claims on Radio 5 Live Breakfast, the Chancellor said: "Look, who is responsible for creating these debts? I didn't rack up these debts. Ed Balls, who actually wants to take my job, is the man who racked up these debts."