Kemi Badenoch has told former Prime Minister Sir Tony Blair to "not waste your time" trying to convince the Labour government to change course.
The Conservative Party leader said Sir Tony was right to ask Labour MPs to focus on a "proper political project that increases our economic and military strength".
But Badenoch claimed there was "only one show in town" to deliver this, as she advised the Labour grandee to vote Conservative at the next general election.
Her letter follows Sir Tony's 5,600 word essay that argued Sir Keir Starmer's government had no "coherent plan" for the country and had introduced policies that held back business. The prime minister has defended his decisions.
Badenoch's open letter published in The Times is the latest contribution to the debate over Labour's future, which has seen essays and opinion pieces published by key Labour figures.
Sir Tony's initial intervention came as Sir Keir faces a potential leadership challenge following a poor set of election results and ministerial resignations.
Badenoch said those vying to replace Sir Keir "will be no better".
She also criticised some of Sir Tony's record in government, including on devolution and the impact of legal reforms on migration.
She said: "The Blairite legacy is that the entire country is now run by HR as Labour junk your best ideas and champion your worst.
"So you're right: we need problem-solvers. It's why I trained as an engineer and later, why I came into politics. I know that real problem-solving starts with diagnosing the root cause. It means facing the facts as they are, not as we wish them to be.
"Well, Tony surely now you must accept that the facts of life are Conservative. There is only one show in town for the political project you proposed."
Badenoch said Sir Tony's essay failed to address the "question of who we are as a nation", adding "culture matters" and "we are more than a series of economic units working to deliver growth".
After she criticised other political parties, Badenoch told Sir Tony: "Don't expect Labour to change. Don't waste your time with these essays."
She added: "If you want serious change at the next election my advice to you - as it is to everyone who is sick of Starmerism - is to vote Conservative."
Sir Tony, who won three general elections, had argued a change of Labour leader was "irrelevant if it doesn't start with a policy debate".
He agreed with some of the government's policies but he offered suggestions for change, including removing parts of the net-zero agenda "which prioritise clean energy over cheaper energy" and reforming welfare.
The former PM said Labour must remove obstacles to business growth, take action to tackle illegal immigration and harness artificial AI.
He called for the party to champion the "radical centre".
Sir Keir delivered a near-3,000 word riposte to Sir Tony on Thursday, in which he said he had made the right policy choices given the backdrop he inherited.
He acknowledged Labour's early decision to restrict winter fuel payments, on which it eventually U-turned, had been a "mistake", and that it had "asked a lot" of businesses by hiking the amount of National Insurance tax they pay.
But he said the party had "got the big political choices right", pointing to falls in migration, NHS waiting times, and knife crime, whilst arguing the UK was "outperforming our peers" economically.
Former health secretary Wes Streeting and Andy Burnham, the Greater Manchester mayor who is seeking a return to the Commons, accused Sir Tony of underestimating the impact of inequality in his critique.
Both men are considered potential Labour leadership challengers to Sir Keir, although no formal contest has been launched and the PM has said he would not "walk away".
Burnham is seeking to become an MP again on 18 June in the Makerfield by-election, on the outskirts of Wigan, in what is expected to be a closely-fought contest with Reform UK's Robert Kenyon.
You can see a full list of the candidates standing in the Makerfield by-election here.
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