He believes that something between a third and a quarter of the party share his views, and he is confident that the core Kinnock-Hattersley statement of party principle, Aims and Values, will not win a two-thirds majority at the party conference in Blackpool.
But any majority would be enough for Mr Kinnock, and that is the source of Mr Benn's fear. For he believes that, when the economic crisis blows, the voters will suddenly become aware of "the plunder of public assets, the waste of oil", and they will then look for an alternative to Margaret Thatcher.
He told The Independent: "My fear is that if there isn't what I call a socialist alternative on offer, people could at that stage be so frightened that they could swing further to the right." He said: "I am very, very nervous also that the Labour policy reviews are moving us closer to the Thatcher position at the time the Thatcher position is beginning to fail."
Labour was failing to attack. "When was the Prime Minister forced to defend herself? There isn't really what I would call an analytical opposition, an ideological opposition, a policy opposition. It's all abusing them and saying, `You can trust us not to ruin it.' I don't think there is a posture likely to win power.
"My fear at the moment is that at a time when a lot of people are worried, interested, want to know what's happening, what could be done, they are not getting anything other than personal abuse of Tory leaders, plus protestations of innocuity; how safe it would be to vote Labour because the Labour Party is getting rid of its left, it isn't going to challenge market forces, it's come to terms with the Single European Act, happy to have the Americans here, and so on."
Mr Benn said: "The policies that are being put forward now by the Labour Party are to the right of the policies of Wilson in his latter years; they are not radical policies. Today, we are saying market forces will do it, and yet market forces and the technological revolution are burning people out. All over the place. I was in Rochdale, where 600 Courtauld's workers were made redundant that very day. It's the same wherever you go. It's like being a stretcher bearer at the battle of the Somme."
Yet, he said, Labour continually distanced itself from workers who were struggling to defend themselves; the miners, the P & O seamen, the postmen, were regarded as an embarrassment.
He talked of the possibility of an unpopular Mrs Thatcher being knifed by her own party, of becoming Countess of Finchley, and he added: "If Mrs Thatcher became unpopular, she might be replaced by Howe or Biffen, a Baldwin figure. We would then be less radical than the Tories in revising Thatcherism."
Mr Kinnock is scornful of such criticism. But Mr Benn said: "The real argument in British politics is between those who are in favour of democracy and those who are not, and the socialist rhetoric is a very minor theme in it. It's like religious sermons; so long as nothing happens between one Sunday and another, the bishops can preach brotherhood or love but it does not affect the establishment. But when you start saying, `Who has got the power, where did they get it from, to whom are they accountable, and how do you get rid of them?' - when you ask those questions, then the fur begins to fly."
But Mr Benn had no intention of backing off, and the strength of the left was growing. "It hasn't got any press whatever, or representation in the BBC or IBA at all, but I don't myself doubt that it is an element in British politics, much stronger than the decaying centre, that has a legitimacy that will no longer be able to be dismissed."
And would Mr Benn remain a pain in Mr Kinnock's neck? "I don't think I am a pain in his neck. I think I am a tree in the garden, which is growing, too."
From the Home News pages of `The Independent', Saturday 24 September 1988