The shadow Treasury minister vowed to “unleash” the party by handing more power to its members, and accused Mr Corbyn of “indecisiveness” and a “lack of leadership”.
Referring to the general election defeat as Labour’s “own Dunkirk”, Mr Lewis said he was standing for leader because “if I don’t, certain necessary truths may go unspoken”.
The Norwich South MP is from the left of the party but has been a key figure in urging the current leadership to adopt a more anti-Brexit position, including supporting a second referendum.
He is a member of the “Love Socialism, Hate Brexit” group of left-wing, pro-EU MPs.
The battle to replace Jeremy Corbyn as Labour leader
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Announcing his candidacy, Mr Lewis claimed that Mr Corbyn had not done enough to make party structures more democratic.
Writing in The Guardian, he said: “Jeremy Corbyn’s first promise as leader was never fulfilled. The party was never democratised on the scale or to the extent that members were led to expect – they were never empowered to campaign, select candidates or determine policy on the scale that was required. This must now change.
“We don’t need foot soldiers, we need an army of activists who think critically, treat each other with respect and have a serious democratic stake in the movement. I don’t want to manage the labour movement, I want to unleash it.”
Mr Lewis said Labour had failed to make a break with the era of Tony Blair and Gordon Brown and had offered a “shopping list of rather disconnected policies” rather than proving to voters in the party’s heartlands that it understood their concerns.
Voicing frustration at the party’s Brexit stance at the general election, he accused Mr Corbyn of “indecisiveness and triangulation”, adding: “Such prevarication and lack of leadership must never characterise our politics again.”
Mr Lewis also said Labour should campaign for electoral reform, pointing out that a majority of voters had backed left-wing parties last week.
He joins Emily Thornberry, the shadow foreign secretary, as the only two candidates to have officially entered the race.
An number of other prominent MPs, including Sir Keir Starmer, Rebecca Long Bailey, Lisa Nandy, Yvette Cooper, Jess Phillips and David Lammy, are all believed to be considering a bid.
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