The party’s candidate has consistently held a solid lead over Conservative rival Zac Goldsmith, who is perceived to have suffered from running a negative campaign that controversially sought to link Mr Khan to extremism.
And shadow chancellor John McDonnell set the Labour Party on the right path for success in the General Election in four years time.
“If we can narrow that gap, we will demonstrate steady progress.
“What we are looking to do is build over the next four years so that we steadily, steadily build our support and then we are ready for 2020.”
Shadow international development secretary Diane Abbott said a win for Mr Khan would be a vindication of Jeremy Corbyn’s leadership. She told The Guardian that in London “more people have heard of Jeremy than have heard of Sadiq. In London it’s all about Jeremy.”
Mr Khan is expected to win the race, out-polling Conservative candidate Mr Goldsmith throughout the campaign.
A final poll by the London Evening Standard released on Thursday indicated Mr Khan would win by a clear 57-to-43 margin.