John Prescott has become the latest senior Labour politician to voice open doubts about his own support for Tony Blair's decision in 2003 to place British military forces behind the American-led invasion of Iraq.

In a wide-ranging interview with the New Statesman magazine the former deputy prime minister asks himself: " I do wonder, looking back now, having the privilege of discussing with Tony about all this, how did I go along [with it]?"

Listening to some of Blair's video-conferences with George Bush was, he admits, a hair-raising experience. "Bush is crap, you know it, I know it, the party knows it," he tells the magazine.

At the time there was little dissent in cabinet from the drift towards war, which the Chilcot inquiry is investigating as part of the long-promised overview on what became Britain's most unpopular military engagement since the Suez affair in 1956.

Clare Short raised questions, as did Robin Cook. He resigned as the invasion began, Short did so later. But most cabinet members said at the time and later that they got all the answers they sought and backed the then-prime minister in the belief that Saddam Hussein did possess weapons of mass destruction (WMD) and the will to use them. That view was both widely held – even by France and Russia at the time – but also disputed.

Prescott, who is not expected to be called as a Chilcot witness, tells the New Statesman: "I did listen to some of the video links between Tony and Bush … and I mean, they can be hair-raising, because Bush has got his own kind of approach … it did make you think."

Visiting the then US vice-president, Dick Cheney, with Christopher Meyer, Britain's ambassador at the time, he was alarmed by the American approach and later came to feel that Blair had not used British leverage sufficiently. "I've often thought, 'Well, you could have just said, 'Sod you … we're not doing it.'" Meyer expressed the same view to the Chilcot panel, whose memoirs were sufficiently offensive about Prescott to prompt a public spat with the man Prescott calls "bloody red socks, that idiot".

Asked if the then attorney general, Lord Goldsmith, was bullied by Blair into approving the war, Prescott said: "If you say, 'Was Goldsmith a happy man about this?' – no, he wasn't ... That's quite different from saying, 'No, I'm sorry, my view is that it's illegal, I'm not supporting it.'"