Under outline plans, the split would start with recurrent revolt against a Euro-sceptic whip, followed by resignation from the party whip, and an eventual alliance with Paddy Ashdown's Liberal Democrats on the Opposition benches in the Commons.
The threat from Mr Clarke and his moderate Tory colleagues last night brought instant denunciation from the Tory right, with a senior figure saying: "We will not be subject to threats of blackmail. If they want to go, good riddance."
One the other side of the deepening Tory divide, one MP told The Independent that up to a dozen Conservative MPs would eventually be prepared to resign the party whip in the Commons if the new leadership froze out pro-European Tories.
"We are beginning the scenario where we separate by stages," he warned. "Rather than trying to bring us in, in a sense they're forcing us out."
That was the message also delivered by Mr Clarke himself last night, when he warned of the threat posed by Mr Hague's efforts to "steamroller" through views that were hostile to Europe.
Earlier, the Clarke camp had circulated a letter sent by Mr Hague to Euro MP Caroline Jackson, in which he ruled out membership of the single currency, under his leadership of the party, for another decade at least.
In a calculated rebuff to Mr Clarke - who could not stomach such a repudiation of the carefully-sculpted "wait-and-see" policy on which the Tories fought the recent election - Mr Hague added: "If I were elected leader of the Conservative Party, I would certainly expect every shadow minister to support this policy."
Pointing to the wording of that letter, one Clarke team member said: "Ken could not serve on those terms."
It is also unlikely that Michael Heseltine or any other pro-European MP could join Mr Hague's team on such terms of abject and unconditional surrender.
Mr Clarke said in a speech to the West Oxfordshire Conservative Association, in Witney, last night: "The person elected next week simply will not have a detailed mandate to impose a series of immediate changes to Conservative Party policy on specific issues."
Nevertheless, he said that both Mr Hague and John Redwood were attempting to claim that they had the power to lock the party into a policy of single- currency rejection.
But the former chancellor of the Exchequer warned: "Attempts to bind the party in advance to hardline positions which are designed to exclude other arguments on the subject will divide and damage us."
That statement hardened the warning issued by Mr Clarke on Thursday night, when he said: "We divide the party if we regard the leadership election as deciding the key issues before the process [of policy review] has even started."
One of Mr Clarke's Commons backers said last night that the party was now facing the real prospect of "staged separation", with a group of up to a dozen pro-Europeans initially defying the party whip and then, if no reconciliation took place, resigning the whip.
"That would be the next stage," the MP said. "Then of course the next stage after that is that you would automatically go into voting alliances with people. We would be sitting with the Liberals, and you'll take it from there."
The MP said a lot would depend on the lead that might be given by Mr Clarke. "If Ken can take it, or find a way through, then the rest of us would be inclined to follow him. But they're making it impossible for him."
That difficulty was robustly put by Mr Clarke in his speech last night, when he said: "My kind of Conservative Party will be a party of all the people, seeking to broaden its appeal, not narrow it.
"If I am elected next week, I will make inclusivity and the search for unity the central hallmark of my leadership of the party. I want us to find a way through the ideological battles that cost us dear in recent years and to unite around the area of maximum agreement.
"We must stress what unites us, to focus our fire on the economy, where Labour will be weak, and to find a way of living together on Europe, rather than steamroller through particular views. My shadow team will be a wide one, representing all strands of Conservative thinking.
"This leadership contest is not - and must not be - about setting straightaway in concrete the policy positions of the Conservative Party for the next five years."
Unfortunately for Mr Clarke, that has already happened, with Mr Hague and Mr Redwood competing for the right-wing vote, with a considerable hardening of Mr Hague's position on the single currency over the last week.
If - as seems certain now - Mr Hague goes through to the leadership next Tuesday or Thursday, the parliamentary party will have slammed the door on Mr Clarke.
The question that would then remain open, if Mr Clarke went on to the back benches, is whether he would use the existing framework of moderate Tory organisation to lead a withdrawal - as Shirley Williams, David Owen and William Rodgers with the Social Democrats in 1981
One of Mr Clarke's Commons allies said last night: "We've already got the Mainstream-Macleod Group operation. It's all staffed and got an office, and there's the Tory Reform Group with branches all over the country. There's quite a substantial part of the party inside and outside of Parliament."Reuse content