The former first minister now believes the Out campaign can win the forthcoming vote because both sides of the debate are dominated by “scaremongering”.
Mr Cameron heads to Brussels this week in an effort to secure a new deal on the UK’s membership of the EU which will then be put to the British people in an in-out referendum, expected to be held in June.
Both sides have started ramping up their campaigns. Foreign Secretary Philip Hammond warned yesterday that Britain will be punished if it leaves by other countries which do not want to see it “succeed” alone.
Mr Salmond, who resigned as first minister immediately after losing the Scottish independence referendum, warned both Mr Cameron and Chancellor George Osborne would face a similar fate if they are unsuccessful in campaigning for an In vote.
Mr Salmond said: “He [Cameron] won’t have a choice in the matter. If he loses the referendum then he will be shown the door – as indeed will be the Chancellor, George Osborne.
“It’s untenable to try and maintain a position if you lose a referendum. They used to say in the Conservative Party a long time ago you have to do the ‘honourable thing’.”
The former SNP leader, who is now the party’s foreign affairs spokesman at Westminster, also agreed yesterday to take part in a televised debate on the EU referendum with Ukip leader Nigel Farage.
Mr Salmond warned that the “Project Fear” approach, adopted by the No camp in the Scottish referendum, had now “divided itself into two” and was dominating both sides of the debate on the UK’s European future.
Mr Salmond said: “They’re flinging their scaremongering at each other.
“If we have that sort of debate over these next few weeks, I think there’s a very real chance that the anti-Europeans will win because the only way that the anti-European forces can win is if we have two campaigns of scaremongering. In that case, the biggest fearmongering tends to win.
“The real danger is that the pro-European case – the real case about this country’s position in Europe – will not be made.”
He warned that the No side lost 17 per cent of the vote during the Scottish referendum and, given the closeness of the polls in the EU vote, Mr Cameron “cannot afford to lose 17 per cent of the vote”.
Mr Cameron heads to Brussels on Thursday in an attempt win the backing of the other 28 member states for the EU reform package drawn up by European Council president Donald Tusk.
It proposes changes in four policy areas which were identified by Mr Cameron as crucial to addressing the British public’s concerns about Europe, including boosting the EU’s competitiveness and asserting the sovereignty of member states.
Plans for new restrictions on benefits for migrant workers and the rights of countries outside the eurozone are more contentious, and Mr Cameron can expect wrangling over the details to go down to the wire at the Brussels summit.
Mr Hammond said there were still “a lot of moving parts” in the draft deal tabled by Mr Tusk, but UK had already secured an exemption from “ever-closer union” and a “major breakthrough” on restricting migrant benefits.
Other EU states recognised that Britain needed a “robust deal” in order to stay in.
Mr Hammond said: “Until a few weeks ago people were telling us it was impossible to have any kind of period in which we treated newly arrived migrants differently from people who were already here.
“But the text that is on the table recognises that there can be a period of four years in which people are treated differently. That is a major step forward.
“What we have still got to discuss is what that difference in treatment precisely is … I don’t think that is going to get resolved before Thursday.”
Mr Hammond said the negotiations would go “right to the wire, with some of these things only being able to be decided by the heads of state and government on Thursday when they sit down in that room together”.
He added: “If we can’t get the deal we will carry on talking.”
Challenged that the proposals on the table fell short of the Conservative manifesto pledge of a four-year ban on migrants claiming in-work benefits, Mr Hammond said: “Let’s look at it in the round. There may be areas where we get more than we expected to get and areas where we get slightly less than we expected to get. But it would be absurd not to look at the package in the round.
“Look at all the pluses, all the minuses and weigh the balance.”
Asked whether a one-year ban on in-work benefits for migrants would be enough to satisfy his party, Mr Hammond said: “A one-year period would not, definitely not, but we’ve got four years, a recognition that there can be different treatment for four years.
“Getting agreement that we can treat new arrivals differently for a period of four years is a major breakthrough in challenging, as we have done, one of the sacred cows of European ideology.”
Mr Hammond said he feared that if the UK left it would have to forge new relationships with a very different EU.
“What I think I fear and many people in Europe fear is that without Britain, Europe would lurch in very much the wrong direction,” he said.
“Britain has been an enormously important influence in Europe, an influence for open markets for free trade.
“I think we would be dealing with a Europe that looked very much less in our image. I think the thing we have to remember is that there is a real fear in Europe that if Britain leaves the contagion will spread.
“People who say we would do a great deal if we left forget that the countries remaining in the EU will be looking over their shoulder at people in their own countries saying, ‘Well, if the Brits can do it, why can’t we’.
“They will not have an interest in demonstrating that we can succeed outside the EU.”