Spokesman says cuts are part of package aimed at increasing wages, after Michelle Dorrell says Tories have lost her vote

The government has been forced to defend its plans to cut tax credits after a former Tory voter broke down in tears on the BBC’s Question Time and accused the party of betraying her and thousands of others.

Michelle Dorrell, a mother-of-four who berated a government minister on the panel of the current affairs programme, later revealed that she was now willing to offer qualified support for the new Labour leader Jeremy Corbyn.

The incident has highlighted the problem the government faces in its plans to inform thousands of families they will lose their tax credits by Christmas, including many who will have been core Tory voters.

Dorrell, 35, who runs a nail bar from her home in Folkestone, said on Friday morning after her appearance in the Question Time audience that the Conservative party had lost her vote, but had some words of qualified support for Corbyn.

Dorrell said: “I think Corbyn is very different and that might be what we need. He does have some policies that are ludicrous – such as getting rid of Trident.

“Corbyn is shaking things up and allowing our voice to be heard but there’s more to be done. We need more normal people like me that have been through the worst and have tried to better themselves.”

Dorrell said she and her four children were entirely dependent on a combination of working tax credits and child benefits because her business did not make a profit. “I get £400 a week in tax credits and child maintenance from my ex-partner and child benefit. And that’s what I live on. What I make from the business goes straight back into it.”

Dorrell, who accused the Tories of telling lies to her and others in a similar situation, said that her intervention on Question Time was a spur of the moment response to what was being said. She added: “I can see myself going into politics in the future. It’s something I’ve thought about.”

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Defending the government’s decision to cut tax credits by £4.5bn, David Cameron’s spokesman said: “The point the prime minister and government is trying to get across is that it’s important you see the changes we are making in tax credits are part of an overall package of changes, designed to ensure we push wages up.”

He added: “It’s worth remembering with tax credits ... they have increased over the years and so the spend on tax credits has gone up and up and up. If we’re going to tackle the overall welfare budget and try to move away from being a high welfare country to a low welfare country, then this is something we have to look at.”

Asked whether Cameron would be making an appointment to meet Dorrell and explain his reasoning, the spokesman said: “The prime minister meets with people from all different walks of life all the time.”

Dorrell was addressing the energy and climate change secretary, Amber Rudd, on Question Time when she said: “I voted for [the] Conservatives originally because I thought you were going to be the better chance for me and my children. You’re about to cut tax credits after promising you wouldn’t.

“I work bloody hard for my money, to provide for my children, to give them everything they’ve got, and you’re going to take it away from me and them. I can hardly afford the rent I have to pay, I can hardly afford the bills, and you’re going to take more from me. Shame on you.”

The House of Commons has approved the cuts to tax credits, with only a handful of Conservatives rebelling against the measures. However, there is unease on the government benches about the number of low-income earners who will lose out and the fact they will be told about the scale of the cuts to their benefits just before Christmas.

George Osborne, the chancellor, has insisted that a typical family with parents working full-time on the minimum wage will be £2,000 better off as a result of a host of changes once the increase in the minimum wage is taken into account.

But the Institute for Fiscal Studies and the Resolution Foundation say the welfare cuts in Osborne’s summer budget will leave some of Britain’s poorest families up to £1,300 a year out of pocket. Paul Johnson, the director of the IFS, has said it is “arithmetically impossible” for workers not to lose out from the cuts.

A number of Conservative backbenchers voiced concern earlier this year about the scale of the proposed cuts to tax credits, raising the possibility of a wider backbench rebellion.

Guto Bebb, MP for Aberconwy, and Andrew Percy, MP for Brigg and Goole, suggested there needed to be more protection for the poorest who face losing government support despite working hard in low-paid jobs.

Both MPs voted for the government’s welfare reform and work bill at its second reading in July, but their decision to speak out about the potential impact of the cuts was seen as a warning signal to Cameron and Osborne not to take the support of Tory backbenchers for granted.