Appointed Minister for the Cabinet Office - and dubbed Mr Blair's "Cabinet enforcer" - in the last reshuffle, Mr Cunningham is understood to have delivered his broadside at the British media with the support and backing of Downing Street.
His remarks, to a press gallery lunch at the Commons, raised more questions about the Government's relationship with The Sun and The Times, controlled by Rupert Murdoch, and the Conrad Black-owned Daily Telegraph, the newspapers that have led the claims of a threat to Britain's veto over tax harmonisation.
"Tony Blair came back from St Malo and read the press and thought something had to be done," said one insider.
Mr Cunningham warned that biased reporting of European affairs was threatening to undermine the Government's negotiations in Europe.
"We want a serious debate about Europe. Let's get some serious facts into the debate. What it fits with is the Europhobic prejudice about what is happening in Europe," he said.
"Everybody's second language in the European Union is English. They [British newspapers] are all widely read. Giving this impression not only of Britain being isolated but Britain being determined alone to defy the whole of the European Union is totally counter-productive.
"If we deliberately isolate ourselves we lose, we have no influence, we are left out of the decision," Mr Cunningham said. "We want a dialogue and we need to build coalitions for what we want to achieve. We can't do that by standing aside."
As Minister of Agriculture, Mr Cunningham said he found that Britain was isolated over the ban on beef. "Our credibility was zero," he said.
Rebuilding support had secured the lifting of the ban. The press claims that Britain faced isolation in resisting tax harmonisation ignored the support for Britain's position from France, Germany, Ireland and Sweden, he said.
Mr Cunningham also complained about recent reports that he was spending pounds 2m on his own office. "It's much more than that," he joked.
He said the Government was spending pounds 60m on the refurbishment of Whitehall buildings, including Admiralty Arch and the Admiralty, to house civil servants from the Cabinet Office after a short lease for their offices in the Treasury building ended.
The minister said he had his own pass to reach the Prime Minister's office from the Cabinet office in 30 seconds.
"Anyone suggesting he wanted to move to offices further away either had to have no understanding of politics or had to be barmy," he said.