Tony Blair has warned the Government spends "zero" time worrying about the Labour Party as he blasted the current leadership for failing to provide a "competitive" opposition.
The former prime minister said Labour had failed in its "fundamental duty to the British people", as he hit out at the "ultra-left" takeover of the party.
In an interview with Labour MPs Ruth Smeeth and Wes Streeting for Progress magazine, Mr Blair also dubbed Brexit "the defining moment in British history" as he appealed for Labour to take a more modern approach.
He said: "We (have) failed in what is our fundamental duty to the British people, that is to be a competitive opposition.
"Just ask yourself one simple question. In the Prime Minister's office, in Tory high command, how much of their time do they spend worrying about the prospect of a Labour victory at the present time? I would guess zero."
Mr Blair added: "We've got to make them wake up every morning and fear us."
Mr Blair said a previous lurch to the left between 1979 and 1983 had "cratered the Labour party".
He added: "I don't want to depress you, but there is a big difference between the '80s and now.
"In the 1980s, the ultra-left never took control. They tried but they failed.
"The moment when Denis Healey beat Tony Benn was the moment when the Labour Party was saved."
The Labour leader between 1994 and 2007 warned the current party was putting its principles before power, arguing it had only won "when it has been at the cutting edge of modernity".
Turning to Brexit, Mr Blair said it was not the answer to the cultural and economic problems of globalisation, warning political parties could "end up in an intellectual and political cul-de-sac".
He added: "We have to say, the Government's got a mandate to negotiate Brexit, but we're going to hold them to account that it's not going to damage jobs, that it's not going to damage the economy."
Asked for his final word for those looking to keep Labour relevant, Mr Blair replied: "Urgency. Because politics moves faster today and Brexit ...it's the defining moment in British history."