The Labour leader said that when the party left office "too many of people of Britain didn't feel as if the Labour Party was open to their influence, or listening to them".
He added: "For me, the most obvious example is immigration. I bow to nobody in my celebration of the multi-ethnic, diverse nature of Britain.
"But high levels of migration were having huge effects on the lives of people in Britain - and too often those in power seemed not to accept this.
"The fact that they didn't explains partly why people turned against us in the last general election.
"We have to move on from New Labour, as well as from this government."
More top news
Tesco faced potential prosecution after admitting overstating its profits in 2014 in an attempt to exaggerate the health of the business.
The female runner almost collapsed towards the end of a half-marathon - but still completed the race with a helping hand or two.
South African anti-apartheid leader Ahmed Kathrada has died at the age of 87.