Mr Agnew labelled the oversight of the scheme “nothing less than woeful” and accused officials of “schoolboy errors” in the administration of COVID-19 financial support.

Speaking in the House of Lords, Mr Agnew accused the government of “arrogance, indolence and ignorance” in its attitude to tackling fraud estimated to cost £29bn a year.

Mr Agnew said his resignation was not an attack on the prime minister but that he could not stay on in his role in good conscience.

He said: “Given that I am the minister for counter-fraud, it would be somewhat dishonest to stay on in that role if I am incapable of doing it properly. It is for this reason that I have sadly decided to tender my resignation as a minister across the Treasury and Cabinet Office with immediate effect.”

Mr Agnew was responding to a question from Labour about the Treasury’s decision. He left the chamber to applause from fellow peers, The Guardian reports.

When asked by the Labour’s Denis Tunnicliffe if he could provide an accurate figure for how much had been written off, Mr Agnew said he was speaking to defend the government, adding: “But I will only be able to do that in part.”

Mr Agnew added that oversight of Covid loans by the business department and the British Business Bank had been “nothing less than woeful”. He said that the department and bank had been assisted by the Treasury, who “appear to have no knowledge or little interest in the consequences of fraud to our economy or our society.

He added that two counter-fraud staff at the business department would not “engage constructively” with his counter-fraud team in the Cabinet Office.

Boris Johnson’s spokesperson said: “We are grateful to Lord Agnew for the significant contribution he has made to the government.

“We’ve always been clear fraud is unacceptable and are taking action against those abusing the system, with 150,000 ineligible claims blocked, £500m recovered last year, and the HMRC tax protection taskforce is expected to recover an additional £1bn of taxpayers’ money.”