The Conservative Party leader upset many Tory MPs by seeking to drive through changes which they believed could have made it too difficult to remove him.
The rule changes to raise the number of MPs required to force a leadership election from 10 per cent of the parliamentary party to 20 per cent sparked a row at a meeting of the 1922 Committee of Tory MPs on Wednesday night.
The leadership had thought that it had won the issue.
But with a rebellion growing, the executive of the 1922 Committee was forced to reopen the meeting yesterday with Mr Hague to agree a compromise formula of 15 per cent.
"He was told that if he didn't back off, he wouldn't get out alive," said one former minister. "It was nothing to do with Europe. People just didn't like being pushed around."
Under the new rules, 15 per cent - 25 Tory MPs - would be required to force a no-confidence motion.
If it was lost by a simple majority of 51 per cent, a leadership contest would be held; the Conservative MPs would vote in the primaries; two candidates would go to a final round with a ballot of the entire membership. The winner would be free from any challenge for a year.
A senior Labour Party source said last night: "The Tories were clearly embarrassed by the fact that the most popular option amongst their MPs was to keep the 10 per cent figure for triggering a no-confidence vote in the leader, because it shows just how many of their backbenchers really don't have any confidence in William Hague."