Rebecca Long-Bailey has said Labour must stop promising to save working-class voters and offer a more optimistic picture of the future, as she seeks to underline how her leadership would differ from Jeremy Corbyn’s.

The shadow business secretary, who is widely assumed to be Corbyn’s chosen successor, cited a couple she met while canvassing in her home seat of Salford who told her they thought Labour just offered handouts.

“They were working class but they’d bought their own house, they’d worked hard, they felt they should be rewarded for working hard, they didn’t want to think that other people were getting handouts,” she told the Guardian as the leadership race kicks off in earnest.

“Whatever people’s incomes are, a lot of the time people don’t see themselves as destitute and struggling, and they don’t want someone to come along and say: ‘I’m going to remove the scales from your eyes, and save you from yourself’. It’s like, ‘I’ve got a job, I don’t need saving from myself, I just want to do a little bit better, thanks!’” she said.

“It’s that hopeful vision, rather than a vision that says we’re going to save you,” she adds, repeatedly using the word “aspirational” to describe what Labour’s message should be.

Long-Bailey has struggled to shrug off the “continuity Corbyn” tag, after saying in an interview earlier in the campaign that she would award the outgoing leader a score of 10/10, despite last month’s crushing general election defeat.

As well as promising to strike a more upbeat tone, Long-Bailey said she would lay more stress on national security than Corbyn.

“My approach to things would be very different. For example, talking about security, I think it’s important to make sure that people know that you’re going to keep them safe. Now that’s what Jeremy was going to do but sometimes that message didn’t come across,” she said.

And she promised to shake up the shadow cabinet, to ensure all strands of Labour tradition are represented, and end the factional in-fighting that dogged Corbyn’s five years at the top of the party.

“I think we do need to have that diversity, because we’ve got some really experienced, amazing people right across the [parliamentary Labour party], as well as those who’ve been in the shadow cabinet up to now and we’ve got to have that good mix of talent in there.”

At a packed rally for Long-Bailey in a Hackney bar on Tuesday evening, some of the loudest applause came when she backed open selections for MPs – with one enthusiastic audience member shouting, “banish the Blairites!”

Confronted with the comment, Long-Bailey insists: “We don’t want any of that … this goes right to the heart of what the party is supposed to be about, and this is what upsets me so much.

“The only way we ever win, is where we represent those elements of the centre-left. That’s why we were created: to bring together all those left groups,” she added.

Long-Bailey’s anecdote about canvassing the aspirational couple in Salford was reminiscent of one told by Blair in his 1996 conference speech, when he said that while campaigning, he had met, “a man polishing his Ford Sierra, a self-employed electrician,” who had told him, “as far as he was concerned, being better off meant being Tory too”.

Play Video 3:45 What do the Labour leadership candidates really stand for? – video explainer

Blair said: “That man polishing his car was clear: his instincts were to get on in life, and he thought our instincts were to stop him. But that was never our history or our purpose.”

Long-Bailey praised Labour’s manifesto, which Ian Lavery – the Labour chair and one of her key supporters – called a “book of hope” as he introduced her at the rally.

But she said the party had failed to be clear enough about its message – and even its purpose. “What does Labour stand for? People said: ‘I’m not really sure’. There were so many great policies but there was nothing to really pull them all together, and say ‘look, this is what Labour will do – the end result will be this, it will be realising your aspirations,’” she said.

By contrast, she said that Boris Johnson’s “Get Brexit done” slogan “went through into people’s psyches” – so much so, that her own seven-year-old son had shouted it out in the supermarket during the campaign.

That appeared to bode ill, if Long-Bailey wins, for the future of senior figures around Corbyn who were meant to be responsible for shaping Labour’s message.

“It’s important for me to have my own team,” she stressed. “Of course you want people who share your own political vision around you, but you also want to have people around you who are experienced, and are capable for the job in hand.”

She said she envisaged, “a very robust press operation that develops our messaging and narrative,” which “will be structurally different from what we see at the moment”.

Amid reports of chaotic organisation during the campaign, she added: “I come from quite an efficient background, so I expect to see an office environment that’s run efficiently.”

Before December’s crushing defeat, it was widely assumed at Westminster that many Labour members would follow Corbyn’s lead in choosing his successor.

But early polls have suggested the shadow Brexit secretary, Keir Starmer, is the frontrunner and he has won the support of two of the big five unions, including Unison and Usdaw.

Lisa Nandy will also be on the ballot paper after receiving the backing of Chinese for Labour, following support from trade unions the GMB and NUM. Long-Bailey is also expected to secure the backing of Unite, Labour’s largest donor, on Friday.

She has generally been regarded by colleagues as one of the more self-effacing members of the shadow cabinet, but she says that following a period of reflection after the election defeat she had decided: “I am the only person to do it.”

She adds: “I’ve always been a grafter in the background; and sometimes it’s the grafter in the background that is the one with the ideas and the vision.”

Long-Bailey and her close friend Angela Rayner are supporting each other’s campaigns: Rayner’s for deputy leader. The pair share a flat when they are in London and Long-Bailey reveals that they first discussed running for the party leadership in a “jokey” conversation several months ago.

“Angela said, ‘If it all goes tits up, you and me will have to sort it out you know: there’s only me and you’ and I said, ‘Don’t be stupid!’

“Anyway, fast forward to the election defeat, and we rang each other up and I said: ‘You know that conversation we had, we probably should have a chat, because you’re probably right”.