Downing Street has risked causing widespread offence by claiming there should be no need for food banks because benefit payments are high enough to pay for such essentials.

Sources at No 10 made their comments after the prime minister, David Cameron, told MPs he was planning to visit a food bank in his constituency – a move almost forced on him by weeks of Labour taunting on the issue.

Speaking after Cameron's announcement at the weekly prime minister's questions session in the House of Commons, a source said food banks were to be welcomed as an example of "the big society".

But she added: "Benefit levels are set at a level where people can afford to eat. If people have short-term shortages, where they feel they need a bit of extra food, then of course food banks are the right place for that. But benefits are not set at such a low level that people can't eat."

The comments are likely to provoke outrage among opposition MPs and poverty campaigners, especially with the government undertaking widespread benefit cuts at a time when prices are rising faster than the economy.

The Trussell Trust, the UK's leading food bank distribution charity, estimates that in the year 2011-12 food banks fed 128,687 people in the UK and it forecasts that will rise to more than 230,000 during this year.

"Every day people in the UK go hungry for reasons ranging from redundancy to receiving an unexpected bill on a low income," says the charity's website. "Rising costs of food and fuel combined with static income, high unemployment and changes to benefits are causing more and more people to come to food banks for help."

The Labour leader, Ed Miliband, used his questions at PMQs to attack the government's economic record after figures this week showed that following a return to growth last summer the economy shrank again in the final three months of last year, by 0.3%. If there is another quarter of falling growth, the UK economy will have entered a triple-dip recession.

"On his watch, because of his decisions, we have the slowest recovery for 100 years," said Miliband, who claimed UK economic growth was the 18th slowest of the 20 biggest world economies, and again urged the coalition to rethink its cuts and austerity programme.

Cameron countered that the government was cutting corporation tax, investing in enterprise zones, and had presided over the creation of 1m apprenticeships and 1m new private sector jobs, adding: "But do we need to do more to get banks lending and business investing? Of course we do, and under this government we will."

He added: "If you listen to the EU, the OECD or the IMF, they will point out Britain will have the fastest growth of the major European economies this year."

The prime minister criticised Labour for not regulating the banks and building up debt during its time in office.