Labour and poverty charities have condemned a government minister as out of touch after he suggested that families living in poverty because of the benefit cap could consider taking in a lodger to make ends meet.

Justin Tomlinson, the junior work and pensions minister, told a committee of MPs that other ways families could cope with the impact of the cap would be to move, or to seek to renegotiate their rent.

Answering questions from the work and pensions committee, Tomlinson also said there was no specific government analysis taking place about the impact on people of the cap, introduced under David Cameron’s government, and reduced in 2016.

The absolute maximum amount of benefits a couple can receive, whatever their circumstances, is £20,000 a year, rising to £23,000 in London.

While the government argues the cap offers an incentive to work and prevents the unfairness of people on benefits receiving more than the average wage, critics say it is pushing many families into extreme poverty and debt.

Questioning Tomlinson and the DWP’s head of working-age benefits, Pete Searle, the Labour MP Ruth George asked what analysis of this effect was being done. Searle said that as part of a wider evaluation of “other outcomes” of the policy, officials were looking into how people “respond to the cap”.

George said: “Responding to the cap – does that include things like having to switch the heating off and be freezing cold at night? Does that include things like not being able to feed their children to a nutritionally decent standard?”

Almost two-thirds of people affected by the cap were not entering work, said George, the MP for High Peak in Derbyshire.

Tomlinson responded: “Of those, some will have made other changes, including in their housing costs, whether that is either moving or renegotiating what their rental housing costs are. Or they could, for example, have taken in a lodger. So there’s other circumstances than work.”

George responded with incredulity: “These are large families; they’ve often got three children in one bedroom. How are they going to take in a lodger?”

While some tenants in social housing are allowed to take in lodgers, for those in private accommodation it usually needs the landlord’s permission, and any income would need to be declared.

Tomlinson’s comments were condemned by the Child Poverty Action Group. Alison Garnham, the charity’s chief executive, said: “Most capped households are single parents with very young children. Almost two-fifths of those parents have a child aged under two.

“The idea that they can either renegotiate their rent with a willing landlord or take in a lodger is frankly illusory. What happens in reality is that they become even poorer and their children lose out.”

Margaret Greenwood, the shadow work and pensions secretary, said: “This shows just how out of touch the government is from the realities of life facing low-income families as a result of its cruel benefits regime.”

A DWP spokeswoman said that when Tomlinson used the example of people taking in lodgers, this did not mean he was necessarily recommending that other people do the same. When asked if this meant Tomlinson was instead recommending they did not take lodgers, she said this was also not the case.

The spokeswoman said: “He gave illustrative examples from departmental analysis of how some households subject to the cap may have supplemented income. It is wrong to suggest that he said that all households under the cap could or should consider taking a lodger.”

Explaining the wider reasons for the benefit cap to the committee, Tomlinson said it had three objectives: saving money; the “fairness test” over comparisons with working incomes; and incentivising work.

This had worked for many families, he said. “For those people where it has made a difference, it has significantly improved their life chances, for not just them but for their children.”

But George pointed out that of those affected by the cap, 81% were not subject to “work conditionality” – meaning that circumstances such as very young children dictate they are not automatically expected to seek work.