On Monday night the Commons will vote on the welfare reforms I set out at the budget. These reforms are a central part of a new contract for Britain between business, the public and the state to create the higher wage, lower welfare, lower tax economy our country needs to see.

We are saying to working people: our new national living wage will ensure you get a decent day’s pay, but there are going to be fewer taxpayer-funded benefits. We’re saying to businesses: we’ll cut your taxes, but in return you must pay higher wages and train our young people for the challenges of their generation. And to the country, we’re saying: we will spend less, but we’ll finally live within our means and deliver economic security.

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I believe this settlement represents the new centre of British politics, and appeal to progressive MPs on all sides to support us. On wages, our national living wage will be worth £7.20 an hour next April and well over £9 an hour by 2020. That will mean a pay rise of up to £5,000 a year in cash terms for 0.75 million on the national minimum wage and a further two million people on low pay. Independent forecasters say 6 million in total can expect a pay rise thanks to a ripple effect higher up the income distribution. This is much bigger and bolder than the minimum wage of £8 by 2020 offered by Labour at the election, so opposing it is opposition for opposition’s sake.

We will cut corporation tax again to just 18% and increase tax breaks for firms that want to invest, ensuring Britain remains the best place to do business in the world. Labour in government actually cut corporation tax; only in opposition do they want to increase it. And because we’re requiring all employers by law to pay the national living wage, we can rein in the tax credit system, which has subsidised low wages for too long.

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To their credit, New Labour work and pensions secretaries such as John Hutton, David Blunkett and James Purnell all tried to reform the welfare system. Now Alistair Darling says tax credits are “subsidising lower wages in a way that was never intended”. And Frank Field, elected by all MPs to be the new chair of the work and pensions committee, agrees that the system as it stands is simply “not sustainable”, and the budget represents a “game-changer”. That’s because, working closely with my colleague Iain Duncan Smith, those long-held aspirations for genuine welfare reform are being delivered.

The new universal credit, replacing six different out-of-work benefits, is bringing some sanity to a system David Blunkett described as “crackers” by ensuring that it always pays to take a job or work more hours. Already there is evidence that those on universal credit are more likely to be in work and to earn more. The benefits cap we introduced in the last parliament has not led to the “social cleansing” some predicted. Instead, of the 58,700 households capped since 2013, more than 22,000 have moved into work or reduced their housing benefit claim.

Overall, the welfare reforms we’ve introduced so far have delivered progressive ends: since 2010, the number of people claiming the main out-of-work benefits is 1 million lower, the number of workless households has fallen, a record number of women are in work, and overall inequality is down.

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Furthermore, anyone who cares about well-funded public services such as the NHS and schools knows we have to control the costs of a welfare system that has become unsustainable and risks crowding out other areas of government spending. In 1980, working-age welfare accounted for 8% of all public spending, but by 2010 it had risen to nearly 13%. While this country has just 1% of the world’s population and produces 4% of its wealth, it accounts for 7% of global welfare spending. That’s not sustainable.

Three in four people – and a majority of Labour voters – think that Britain spends too much on welfare. For our social contract to work, we need to retain the consent of the taxpayer, not just the welfare recipient. For those who can work, I believe it is better to earn a higher income from your work than to receive a higher income from welfare: better for individuals, better for families, better for taxpayers and better for our whole society.

We will protect the most vulnerable – disabled people, pensioners, who cannot change their circumstances, and those most in need. But it can’t be right that a tax credits system Gordon Brown said in its first year would cost just over £1bn a year ended up costing £30bn a year, with payments being made to nine in every 10 families with children. That’s not what our welfare state was designed for, and Britain can’t afford it. Our reforms mean tax credits will go to five out of 10 families, not more. Who can seriously argue that that’s not enough?

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And surely it’s fair that families relying on welfare are confronted with the same choices as those who rely solely on their earned income, and have to think hard about whether they can afford to have more than two children. Now that we are able to support families by providing free childcare, surely we can ask lone parents to prepare for a return to work when their child reaches three – an extension of a reform first advanced by Purnell?

You have to believe in an unaffordable welfare state that has departed very far from the original principles of William Beveridge, and ignores the need for taxpayer consent, to oppose these commonsense proposals. I thought British politics had taken a step forward when Labour’s acting leader, Harriet Harman, indicated that she would support at least some of our reforms. She accepted the need for a lower benefit cap and the limit on the number of children eligible for tax credits, arguing that Labour cannot continue to ignore voters’ views on welfare.

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She recognised something else important in a democracy: that oppositions advance only when they stop blaming the public for their defeat and recognise that some of the arguments made by political opponents should be listened to – just as a previous Conservative opposition realised 15 years ago when it accepted the case for a minimum wage.

Depressingly, the Labour leader has been forced to retreat from her sensible position after Len McCluskey accused her of “running up the white flag” and the leadership candidates Andy Burnham and Yvette Cooper joined Jeremy Corbyn in undermining her. With the vote coming on Monday night, I urge moderate Labour MPs not to make the same mistake as in the last parliament, when they refused to support each and every welfare reform we proposed. I say: vote with us.

Lower welfare in return for a national living wage is widely recognised as a fair deal. It has been proposed on the left as well as the right. Welfare reform is not just about saving money. It’s about transforming lives, and social justice. This is the new centre of our politics. All those who call themselves progressives should join us.

• This article was amended on 27 July 2015. An earlier version stated that “That will mean a pay rise of over £5,000 a year in cash terms for the 2.7 million people currently on the minimum wage...” This has been corrected.

