Video report by ITV News Political Correspondent Romilly Weeks
Sir Keir, who is way ahead in the race's first stage with 68 colleagues backing him, has already made it through to the second stage by securing the backing from at least 22 - or 10% of - Labour MPs and MEPs.
In a bid to win over the current leader's supporters, Sir Keir told an audience in Manchester as he formally launched his campaign, that Jeremy Corbyn was "right" to position Labour as the "party of anti-austerity".
"We are not going to trash the last Labour government, but nor are we going to trash the last four years - there have been very many important moves," he said.
"Jeremy Corbyn made our party the party of anti-austerity and he was right to do so."
Ms Long Bailey, who is also in the race's second stage with 26 colleague nominations, is backed by left-wing Momentum as the "only viable candidate" for leader able to build on the party's "socialist agenda".
The grassroots movement which propelled Mr Corbyn to the Labour leadership is also recommending its members support shadow education secretary Angela Rayner as deputy, arguing the two would work well together to form a "united front against the Tories".
Momentum will now ask its members whether they agree with the recommendations, with ballots - consisting of just two questions - to be sent out early next week.
The group's support for Ms Long-Bailey is unsurprising given that she has long been the favoured candidate of the left to take on Mr Corbyn's mantle.
Speaking at a Labour event in Staffordshire, she said: "I'm not anybody's continuity candidate, I'm principled and it's my principles that have led me here, not my personal ambitions."
She and Sir Keir will be joined in the leadership contest's second stage - where candidates are required to gain backing from grassroots Labour parties and trade unions - by Jess Phillips and Lisa Nandy.
But it looks like the remaining contenders may struggle to get the required 22 signatures to make it through to the next round.
Emily Thornberry has 10 signatures and Clive Lewis is slumping further with just four.
When asked, both gave current Labour leader Mr Corbyn a poor rating out of 10, with Mr Lewis scoring him six and Ms Thornberry giving him zero.
But Sir Keir has refused to rank Mr Corbyn's leadership, saying doing so "trivialises" him.
"Jeremy Corbyn led us through really difficult times as a Labour Party. He positioned us in the right place on anti-austerity but we lost the election and now he is stepping down. That is the right thing to do," he said.
"I am not going to get into ranking Jeremy Corbyn out of 10. I think it trivialises him. He is a friend and a colleague. I respect him, thank him for what he has done, but we are moving on now."