The work and pensions secretary, Therese Coffey, has been accused of not understanding the universal credit system after she said people who would lose GBP20 a week in payments next month would only have to work two hours extra to make it up.

In a round of media interviews on Monday, Coffey said she was entirely happy with the plan, which charities and others have warned will notably worsen poverty. She added that people could consider moving to better-paid sectors such as construction.

Asked about the end of the GBP20-a-week increase, brought in to assist people amid the Covid pandemic, Coffey said: “It’s a temporary uplift recognising the reason that it was introduced is coming to an end.”

She told BBC Breakfast: “I’m conscious that GBP20 a week is about two hours’ extra work every week – we will be seeing what we can do to help people perhaps secure those extra hours, but ideally also to make sure they’re also in a place to get better paid jobs, as well.”

Angela Rayner, Labour’s deputy leader, tweeted that this was not true, and Coffey “either knows she’s lying or shouldn’t be in the job”.

Rayner wrote: “An additional GBP20 for a UC claimant isn’t 2 hours work, that’s not how the taper works. An extra GBP20 would require GBP50+ worth of hours, that is how the UC system works.”

The UC taper rate is 63%, meaning that for every pound someone is paid above a work allowance, their benefit is reduced by 63p.

Coffey said people losing out could benefit from government investment in infrastructure projects, which she said totalled GBP650bn and would support 425,000 jobs, adding: “We can want to try and help people get on into those better-paid jobs, often in construction but other elements as well that go alongside these big major projects.”

She added: “It’s a temporary uplift, realising the reason it was introduced. That’s come to an end, that reason. We’re seeing record numbers of vacancies. We’re seeing elements of employment continuing to go up, and I’m confident the 27,000 work coaches we have across the country will be helping people not just get back into work, but to progress in work as well.”

In an earlier interview on Sky News, Coffey was asked if she was entirely happy with the end of the uplift, and answered: “Yes.”

The cut, which will affect about 6m households, has been described by Labour as the largest benefit cut in the history of the welfare state.

Labour will force a symbolic vote on the issue in the House of Commons on Wednesday, although none is formally needed for the government to implement the policy.