Thatcherites, including supporters of Michael Portillo, are furious at Mr Hague's declaration that free market solutions were not the answer to the nation's problems in health, education and welfare.
The anger on the Tory right prompted speculation at Westminster that Mr Hague would face moves to oust him this summer unless the party does well in next month's council elections and the European Parliament poll in June.
"We are livid," one right-wing MP said last night. "I had always assumed Hague was safe until the general election. Now I am not sure."
One senior Tory predicted an outbreak of "mass panic" by Tory MPs who feared the party could do even worse at the next general election than in its 1997 rout.
Mr Hague's critics claim his rejection of the free market has been driven by the party's focus group discussions with voters who see the Tories as "uncaring" on public services.
"He is just flailing around in a thousand different directions," said one Thatcherite. "If Lady Thatcher had been driven by focus groups, she wouldn't have done anything." To make matters worse, some members of Mr Hague's Shadow Cabinet were incensed that they had not been consulted over the policy change. But Mr Hague's aides insisted the row had been defused and were unrepentant about the new policy.
"We will announce radical policies, but we needed to clear the ground first by nailing the lie that we want to privatise everything," said one senior source. "What do the critics want us to say - that we will flog off all the hospitals?"
There were also rumblings of discontent that Mr Hague endorsed Mr Lilley's break with the Thatcher legacy at a dinner in honour of Baroness Thatcher on Wednesday.
Tories who attended said yesterday that Mr Hague's opening speech was "20 minutes too long" for an audience which had come to worship their political heroine, who spoke after him. They said there were "rumblings of discontent" among guests who failed to pay full attention to Mr Hague's speech.