In his speech at the Hay Festival on Saturday, Mr Miliband suggested that Sir Keir had not gone far enough to “incentivise wealth creation”, deliver welfare reform “that does not result in a million people losing work, education or training” or make the UK a “destination for globally mobile capital”.
Mr Miliband said that without these changes it would not be possible to build the “rocket boosters” needed to “supercharge” the economy.
“I didn’t discuss that with him.”
And in a sort of veiled criticism of Sir Keir's perceived inability to communicate his vision, he added: “I am a firm believer that politics is ultimately about the cause. What is your cause? Secondly, what are your signature policies – high-dose, high-impact signature policies – and thirdly: explain, explain, explain.”
Although Mr Miliband occasionally comments on British politics, it is rare for him to be so direct in his criticism.
During the event, he twice declined to rule out a return to frontline politics when questioned by members of the audience.
He said: “As for my own situation, since you asked, I have always said the same thing: I will do my professional work where I can best implement my values, provided I am absolutely committed to being a good father and a good husband.”
“That's always the answer I give. I feel like I'm trying to respect that, so I really appreciate what you said. Please just accept the integrity of my answer.”