Universal credit cannot be solely blamed for the rise in food bank use in areas where the benefit is being rolled out, the minister for employment has said.

Alok Sharma was responding to a report from a committee of MPs that found the Department for Work and Pensions (DWP) had a “fortress mentality” that prevented it from tackling the “unacceptable hardship” created by the switch to universal credit.

With the chancellor under intense pressure to act in his budget next Monday to cushion the impact of the new system, the public accounts committee said the government had ignored the concerns of those affected.

Universal credit is the most radical change to Britain’s welfare system in decades, rolling six benefits into one, which is paid in arrears to mimic a monthly wage packet.

Speaking on BBC Radio 4’s Today programme, Sharma insisted the message he was getting from jobcentre staff and claimants was that they were much happier with universal credit.

However, he refused to comment when told that a report by a charity that runs more than 400 food banks had found they were four times as busy in areas where the full universal credit service had been in place for 12 months or more. The Trussell Trust recorded an average 52% increase in the number of three-day emergency food packages distributed.

Asked about it three times, Sharma said another report by MPs had suggested there were “very many reasons” why people used food banks and they could not be attributed to just one factor.

Sharma rejected claims that his boss, Esther McVey, had been ducking out of media appearances, and said he was responsible for the government’s benefits policy, which he claimed was working because “cliff edges” that had previously put people off working had been removed.

He said he had been visiting jobcentres, most recently in Harlow, Essex, adding: “There are absolutely brilliant people in DWP working as work coaches and they tell me that for the first time in their lives they are doing what they came in to do, which is to provide that one-to-one support which wasn’t available under the legacy system, and that’s a message I get from claimants when I talk to them.”

Separately, analysis by the campaign group 38 Degrees claimed that as many as 39 Conservative MPs, including Sharma, could lose their seats as four million people have their income reduced because of the benefit changes.

The group highlighted the constituencies where the number of people who could be moved on to UC was significantly higher than the majority held by the incumbent MP. In 39 seats it was at least double the majority; in 23 of those seats, it was five times higher.

Those said to be at risk included one of the key architects of UC, the former Conservative leader Iain Duncan Smith, whose majority of 2,438 was significantly outweighed by the 6,180 households expected to be moved on to UC. Sharma is defending a majority of 2,876 in a constituency where 6,567 households were expected to feel the impact of the shake-up.

The chair of the public accounts committee took evidence from charities and local authorities, which told MPs they had seen sharp increases in rent arrears and food bank usage among new recipients of universal credit, not least because of the five-week wait for the first payment.

The DWP’s own survey found 40% of people were experiencing financial difficulties eight or nine months into their claim, and McVey, the work and pensions secretary, recently admitted the rollout would leave “some people worse off”.

But the committee said McVey’s department had repeatedly been unresponsive to on-the-ground evidence about the practical problems with universal credit, and what it called the “unacceptable hardship” faced by many.