David Cameron has falsely claimed the Labour party pledged to privatise Royal Mail in its manifesto for the 2010 general election.

As he faced intense pressure from Ed Miliband, who branded the prime minister the "dunce of Downing Street" after a National Audit Office (NAO) report said the government had dramatically undervalued Royal Mail, Cameron dismissed the attacks by wrongly claiming that Labour had called for privatisation in its manifesto.

The prime minister picked up on Miliband's claim that the privatisation of Royal Mail was a "sale nobody wanted and nobody voted for". Cameron said: "It was in his manifesto. It was a commitment of the last government. They are shaking. They failed to do it but this coalition government privatised the Royal Mail, created thousands of new shareholders and have a great business working for Britain."

The prime minister's remarks are directly contradicted by the Labour manifesto, which called for extra investment for Royal Mail within the public sector. The manifesto said: "The Royal Mail and its staff are taking welcome and needed steps to modernise work practices. For the future, continuing modernisation and investment will be needed by the Royal Mail in the public sector."

The prime minister appeared to have mixed up the chronology over the last Labour government's handling of the Royal Mail. The former business secretary Lord Mandelson attempted to privatise the Royal Mail. But he lost an internal battle and the plan was shelved.

Labour's response to Cameron's claim that Royal Mail sell-off plan was in their 2010 manifesto:



Cameron just wrong that 2010 Labour manifesto included commitment to sell off Royal Mail. Here's what it said. #PMQs pic.twitter.com/PH9hgZh2dL — Labour Press Team (@labourpress) April 2, 2014



Miliband was scathing about the privatisation of Royal Mail after an NAO report earlier this week said the government's determination to sell it cost taxpayers £750m in one day alone. It said the business secretary, Vince Cable, pressed ahead with plans to privatise Royal Mail at 330p-a-share even though there had been warnings that it was undervalued.

The Labour leader said: "He sold at 330p and this morning the price was 563p. It is basic maths – not so much the Wolf of Wall Street, more the Dunce of Downing Street."

The prime minister hit back: "I will take a lecture from almost anyone in the country about the sale of Royal Mail but not from the two muppets who advised the last chancellor on selling the gold. There they sit – not a word of apology for £9bn wasted. The Royal Mail privatisation has got £2bn for the taxpayer, 140,000 employees owning shares, 700,000 members of the public who are now shareholders. This is a great success for our country."

But Miliband accused the government of arranging a "mates' rate" as he said that the undervaluation of Royal Mail had lost the taxpayer £1.4bn.

"A third of the shares were sold to just 16 City investors. Get this: there was a gentlemen's agreement that those City investors wouldn't sell the shares. What happened? Within weeks, half of those shares had been sold and they had made a killing worth hundreds of millions of pounds. In other words, mates' rates to his friends in the City."

