Senior figures are concerned they could be ousted from power if Tory and Reform UK voters come together and the country is hit with economic turmoil.
The race to succeed Rishi Sunak as Conservative leader is expected to begin in earnest this week when the rules for the contest are announced.
Tories say Sir Keir's victory is "skin deep and built on sand" because only around one in three voters backed Labour with just six out of 10 eligible adults taking part in the election.
A Labour MP said: "I think it will be a one-term Labour government."
Warning of the shallowness of support for Labour, they said: "There's a total blind spot in the Labour Party about how bad that result really was for us."
A key worry is that Labour's economic plans hinge on an acceleration in economic growth.
"Every government has gambled on this growth unicorn," they said. "It's never turned up."
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Denne historien er fra July 21, 2024-utgaven av Sunday Express.
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