George Osborne averted a rebellion from his own backbenches last night as Conservative plans to cut tax credits passed by 35 votes.

Several Conservative MPs expressed concerns about the impact the cuts would have on the low-paid. However the Chancellor persuaded MPs to back his plans, promising he would address their concerns.

"I went to see the chancellor expecting to have the thumb screws applied," said one Conservative MP who decided not to rebel after meeting the chancellor.

"But instead he listened and said he would work hard to address our concerns about low-paid workers," he told the Guardian.

In the end only David Davis, who came second to David Cameron in the 2005 leadership race and Stephen McPartland, MP for Stevenage, voted against the proposals. Andrew Percy, another Conservative MP, abstained.

The cuts to the tax credit system were announced by the chancellor in the summer budget and the House of Commons voted in favour of his plans last night by 325 votes to 290.

The current system, introduced by Gordon Brown when he was chancellor, mean that those on low wages and those with children receive payments with the aim of relieving poverty.

The amount received depends on current circumstances and household income. It is reduced by 41p for every £1 that income rises about a certain threshold.

The government's proposed changes will mean the threshold at which payments are reduced will be lowered (from £6,420 to £3,850 for working tax credits) and the rate at which payments are reduced will quickened (from 41p for every £1 earned to 48p for every £1 earned).

Labour's Seema Malhotra, shadow chief secretary to the treasury, said the cuts were "disgraceful" and would impact working families all over Britain.

"This is a political decision made by the chancellor that is set to see over three million families lose an average of £1,000 a year," she said.

"It is ideologically driven, it is cynical and it will directly increase levels of poverty in Britain."

However Osborne insisted other measures announced in the summer budget would offset these changes. He pointed to his "national living wage" which would give 2.7 million people a pay rise and have a "ripple effect" of pay rises all along the income scale.

Treasury minister Damian Hinds said eight out of 10 households would be better off by 2018-9 as a result of measures announced in the Budget.

Frank Field, chair of the work and pensions select committee, said the changes meant the Conservatives had reneged on being the party of working people.

"In one single move [the chancellor] has destroyed his 2020 election strategy because we heard the very powerful speeches the chancellor made saying the Conservative Party was in favour of those individuals who got up in the morning, who did grotty jobs for very low pay and they passed the windows of their neighbours whose curtains were still drawn, who were on benefits.

"Those individuals who still rise to the work motive in this country, which is so important for both economic and human advance, will know as they pass those windows with the curtains drawn they do so on average with £1,300 a year less in their pocket."