Britain's biggest food bank provider has seen a surge in donations after a Mail on Sunday article criticised the charity for failing to run proper checks on people claiming food parcels.

Before the article, there had been about 250 public donations since the Trussell Trust launched its JustGiving page in late January. That jumped to more than 3,300, worth more than £36,000. Several donors cited the article as the reason for contributing.

"The Mail on Sunday story appalled me. This is the least I can do to apologise for their crime," said Anonymous after donating £10.

Another, Spitting Feathers, said: "I am incensed by the disgraceful article. Call this journalism? I don't. I'm not a Christian and admire the work being done by human beings for their fellow human beings. Thank you."

The Mail on Sunday said it carried out an investigation which found that volunteers did not carry out adequate checks on those who claim vouchers and one of its reporters obtained three days' food simply by telling staff at a Citizens Advice bureau – without any proof – that he was unemployed. Many claiming food parcels were also asylum seekers, the paper reported.

The newspaper also cast doubt on the trust's widely reported claims that almost 1 million people would use one of its food banks this year, up 163% on the previous year and part of a trend that has seen use of the trust's food banks increase tenfold since 2010.

Officials at the Department for Work and Pensions accused the trust of "misleading and emotionally manipulative publicity-seeking" and "aggressively marketing their services". But David Cameron has praised the provision of food banks, indicating the government's ambivalent attitude towards them.

Chris Mould, chairman of the Trussell Trust, told the Observer the prime minister had a constructive half-hour meeting with the charity in February. Iain Duncan Smith, the work and pensions secretary, had refused to deal with the charity, accusing it of scaremongering and advancing a political agenda.

Christian leaders have increasingly put pressure on the government to tackle food poverty and recently signed a letter demanding action from ministers and the archbishop of Canterbury, Justin Welby, mentioned food banks in his Easter Sunday message.

"In this country, even as the economy improves, there is weeping in broken families, in people ashamed to seek help from food banks, or frightened by debt," he said.

As for the Mail on Sunday article, the trust said in a statement – given to the paper before publication – that they disapproved of the methods the paper used to get its story.

"The Trussell Trust feels that these undercover methods used to enter the premises of our voluntarily run food banks is an unacceptable attempt to tarnish not only the name of the Trussell Trust, but also the valuable efforts of the 30,000 volunteers who selflessly give up their time to provide a valuable service to people in real need"

Following the surge in donations, first reported on the BuzzFeed news site, the Trussell Trust tweeted: We're blown away by the response to the article on Twitter! Over £15,000 raised for Trussell Trust's Easter appeal #THANKYOU