Conservative leader Kemi Badenoch has denied her party’s plans to cut housing benefit would make people homeless, but suggested some would have to “move somewhere cheaper”.

At Prime Minister’s Questions on Wednesday, she had challenged Andy Burnham to commit to spending 3% of GDP on defence by 2030, saying the cost could be covered by cuts to welfare.

The Conservatives have claimed £4bn could be cut from the housing benefit bill, in part by allowing tenancies in areas where housing is expensive to come to an end.

Asked whether she would be willing to make people homeless in order to fund defence, Badenoch told BBC Radio 4’s Today programme the party would “protect existing tenants”.

During PMQs, Burnham argued national security “can’t come at the expense of social security”.

He repeated that a target date for increasing defence spending to 3% of GDP would be announced in the spending review in the spring.

The PM insisted he would get the welfare bill down in “the Labour way”, by boosting council housebuilding, supporting young people into work and providing more mental health support.

Badenoch said the government should cut housing benefit to fund defence spending now, adding she would exempt pensioners and existing tenants from the plans.

Speaking on the Today programme, she said: “What we’re doing is making sure that people are protected, but capping the amount that people get on benefits because we need to look after our national security.

“Without national security, there aren’t going to be any benefits. We’re all going to be in danger, far more people will be homeless, and the government’s first duty is defence of the realm.”

Her proposed changes would be part of a package that would cut £23bn from welfare to partly fund an increase in defence spending.

In an interview with BBC Breakfast, Badenoch was asked who would be affected by her plans to cut housing benefit.

She said: “We have people who live in areas that are quite expensive and if people need local housing allowance they will need to move somewhere cheaper.

“I think you should aspire to live wherever you want to live, but you shouldn’t aspire for the government, i.e. other taxpayers, to pay for you to live wherever you want to live…

“We’re not removing people from homes – this doesn’t cover pensioners, it doesn’t affect existing tenants – but I do think you need to be fair.”

Responding to Badenoch at PMQs, Burnham said the policy would worsen homelessness.

He said: “I don’t think, myself, that taking £4bn out of housing benefit is going to get the right consensus around this issue because that would create levels of homelessness in this country… that we wouldn’t have seen before, hundreds of thousands of children in temporary accommodation.”

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