A YouGov poll published earlier this week found many Labour supporters were dissatisfied with the selection of Livingstone as Labour's mayoral candidate, with 25% of those polled who voted Labour at the 2010 general election saying it should have picked somebody else.
The poll showed Johnson ahead of Livingstone by two percentage points despite the Labour party at Westminster having a lead in the capital over the Conservatives of 19 points, with 11% of Labour supporters surveyed saying they intend to vote for the incumbent.
King lost to Livingstone by a margin of more than two to one after being his only rival for the mayoral candidature in the selection process run concurrently with the Labour leadership process, which saw Ed Miliband confirmed as leader a day later.
She believes the party nationally would benefit from the momentum of a mayoral victory, just as Johnson's victory four years ago prefaced the Conservatives entering government two years later.
"Of course it is important for Labour to win in London if you want a Labour government," said King. "I am doing this because Ken asked me, because I want to see change on the ground for young people, and because I really want to see Ed Miliband as the Labour prime minister, so for me it is a three-for-one deal."
She said the approach by Livingstone's team was made last year, but the announcement was delayed while she was adopting a baby daughter, her third child, which was finalised on Tuesday.
King, who is on maternity leave from her job as diversity executive at Channel 4, said it would be "jumping the gun" to decide now whether she would serve as a full-time paid adviser to Livingstone if he becomes mayor.
Her brief would include overseeing Livingstone's pledge to restore a London-wide Education Maintenance Allowance, working with businesses to promote Saturday jobs, and providing safe places for young people who are threatened by gangs and violence.
Written by Hélène Mulholland, political reporter and published in the Guardian on 26 April 2012