The government has defeated a Labour attempt in the Commons to force the release of its analysis of the impact of universal credit, in a sign of renewed Conservative unity in defending the much-criticised policy.

The “humble address” motion by Labour, which sought access to briefings or analyses showing the effect on claimants’ incomes and debt levels, was defeated by 299 votes to 279 after four hours of debate.

Those voting with the government included six DUP MPs, despite concerns in No 10 that the party could start to obstruct Theresa May in parliament because of Brexit objections. No Conservatives rebelled.

Labour has used humble address motions on recent issues such as forcing the release of Brexit impact assessments, with the government often not taking part in the vote. But on this occasion Tory MPs were whipped to see off the move.

Esther McVey, the work and pensions secretary, used her response to the motion to take a bullish line in defending universal credit, which is intended to simplify the benefits system and provide greater incentives for work but has recently been criticised by John Major and Gordon Brown, among others.

This week it emerged that McVey had slowed down the expansion of universal credit, which is intended to replace six separate benefits payments. While its use by new claimants will continue to be rolled out, the process of migrating people from existing benefits has been delayed, with only 10,000 moved during 2019.

The government was “learning from that evidence, we are building on that evidence, and we are making decisions so we can improve the system as it goes further,” McVey told MPs.

She vigorously defended the change and condemned Labour for its policy of wanting to scrap it. “That is what this government are doing – getting people into work and turning the corner of more wage growth. We will continue to roll out universal credit, and we will engage with colleagues across the house,” she said.

Introducing the humble address, the shadow work and pensions secretary, Margaret Greenwood, said universal credit was “causing immense hardship wherever it arrived. “It is hard to believe now, but universal credit was designed to lift people out of poverty and smooth the transition into work to ensure that it always pays,” she said. “The reality is that universal credit is a vehicle for cuts.”

She said given that McVey had reportedly told fellow ministers that a number of people moving to universal credit could end up worse off, it was imperative for MPs to see the government analyses of what might happen. “People have a right to know.”

A series of Labour MPs reiterated the argument, with Angela Eagle saying universal credit was causing “undeniable and massive hardship” in her Wallasey constituency, pointing to a 34% increase in food bank use locally since it was rolled out.

In a statement after the vote, Greenwood said the Conservatives had “voted to shamefully cover up the impact that universal credit is having on families and people who most need our support”.

Despite rumblings of discontent from some Conservatives, and John Major’s prediction last week that a botched expansion of universal credit could be as damaging to the party’s electoral appeal as the poll tax was in the 1980s, McVey received almost unanimous support from Tory backbenchers.

Some Conservatives spoke to concede that universal credit needed tweaks, but also praised the principle behind it and in some cases vehemently condemned Labour’s tactics.

However, some Tory backbenchers were more circumspect. Nigel Mills, the MP for Amber Valley, called for a delay in extending the benefit to more people until work was completed to “take out those rough edges”.

Heidi Allen, who represents South Cambridgeshire, called for some significant changes, including an end to first payments being made several weeks in arrears. She said that rather than offer people advances that they then needed to pay back, the benefit should arrive instantly, based initially on an estimate of circumstances.

“I believe it would tackle the majority of debt and food bank use cases that we do hear about. Let’s just do it,” Allen said.

The Waveney MP, Peter Aldous, said the initial rollout of universal credit to part of his constituency had led to numerous complaints, and even now his office was receiving three new problems a week.

“It is clear that many people, often the most vulnerable in society, have been put through enormous pressure and have faced real challenges in getting by on a day-to-day basis,” he said.