The report by the trust, which has more than 400 food banks in Britain, showed the number of people given three days’ emergency food by the Trussell Trust rose from 2,814 in the 2005-06 financial year to 61,468 in 2010-11, 346,992 in 2012-13 before jumping sharply to 913,138 in 2013-14 – including 582,933 adults and 330,205 children.

Figures for 2014-15 are set to be published on Wednesday and are expected to show another increase.

Rachel Reeves, Labour’s shadow work and pensions secretary, has written to prime minister David Cameron challenging him to promise to reduce the number of people using food banks during the next parliament in 2015-2020.

“Under your Government, too many working people are being paid so little that they can’t afford to feed their families – with 1.5 million more in jobs paying less than the living wage and a huge rise in the number of people on zero-hours contracts. And too many people who should be supported by our social security system are being let down by it – with delays in benefit payments, unfair benefits sanctions and the bedroom tax pushing people to the doors of food banks,” the letter reads.

The Conservatives have defended the changes they have made to the welfare system under their policies of austerity.

“We know that many families are facing tough times as a result of the great recession of recent years. When people are struggling it is right that both government and organisations in the community offer support. Unlike Labour, we have allowed Jobcentres to signpost people to food banks. We are also helping to provide emergency financial help to those in desperate need and tackling the real causes of poverty by getting people into work and tackling welfare dependency,” said a Conservative spokeswoman.

There are also some Tories who blame the increase in the number of people using food banks on the food banks themselves, saying that increased supply is fuelling demand.

But the food banks themselves say this is not the case and they represent the “tip of the iceberg” of a real and growing need.