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.
Start din 7-dagers gratis prøveperiode på Magzter GOLD for å få tilgang til tusenvis av utvalgte premiumhistorier og 9000+ magasiner og aviser.
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Brownhill brilliant for Parker's men
SKIPPER Josh Brownhill's insatiable appetite for goals made it nine unbeaten games on the spin for Scrooge-like Burnley.
Japan favours 39 authentic flavours of UK
A TRADING breakthrough means much of Britain's best-loved food and drink could soon appear more often on menus in Japan.
Alarm over 'epidemic of loneliness'
FEELING lonely at Christmas could affect around 32 million people, research suggests.
Great War airfield can reach for skies once more
THE best preserved First World War airfield has secured its future for another year thanks to the generosity of the public.
Sir Elton won't let the sun go down on writing new songs
SIR ELTON John has revealed he is working on new songs despite having quit touring and suffering a severe infection that has left him unable to see out of his right eye.
World Cup hero George dies
TRIBUTES have flooded in for George Eastham, a member of England's winning 1966 World Cup squad whose death was announced yesterday.
Should I quit while I'm ahead, ponders Lesley as 70th looms
SOPRANO Lesley Garrett has revealed her impending 70th birthday has made her think about quitting singing.
French truckers' threat over checks for migrants
SURLY French lorry drivers have threatened to block goods from entering the UK unless checks to stop migrants arriving become more lenient.
Biden could save 40 from death row
PRESIDENT Joe Biden is considering commuting the death sentences of most - if not all of the 40 prisoners awaiting execution in US federal jails, it has been revealed.
'Time to come clean on mystery drones'
DONALD Trump has urged President Joe Biden to explain thousands of sightings of mysterious, SUV-sized drones reported across at least five US states.
