Diane Abbott will continue to be a key figurehead in Labour’s general election campaign, the party has indicated, despite a stumbling radio performance in which she struggled to explain how a pledge to hire 10,000 extra police officers would be funded.

The shadow home secretary tripped up when asked by LBC host Nick Ferrari how much the key law and order pledge would cost. She initially suggested the bill would be just £300,000, before repeatedly correcting herself.

Eventually, Abbott appeared to find the right page in her briefing notes, and gave the full costing for the policy at £298m a year by the end of the next parliament.

She said: “In year one we are getting ready to recruit, but in year two the cost will be £64.3m. In year three, the cost will be £139.1m. Year four, the cost will be £217m and year five, the cost will be £298m and that can be amply covered by reversing the cuts in capital gains tax.”

The Conservatives seized on Abbott’s stumbling performance as evidence that Labour cannot be trusted with public money – a claim the shadow chancellor, John McDonnell, has been keen to shrug off since Jeremy Corbyn became leader.

Corbyn defended Abbott, who is a close political ally and was promoted to shadow home secretary in October – when Andy Burnham stepped down to fight the Manchester metropolitan mayoral election. Asked about Abbott’s interview on Tuesday, Corbyn said he was “not embarrassed in the slightest”.

Labour sources added that the interview was one of many Abbott had given on Tuesday, and the failure to get the figures right initially was an uncharacteristic slip-up from an effective media performer.

Abbott herself later said she had “mispoken”. She suggested media coverage of the slip-up had exaggerated its importance, and what really mattered was the substantive policy, which Labour insists it can fund in full.

The policing pledge was the latest of a series of high-profile policy promises from Labour in recent days, including removing the cap on NHS pay; giving children free school meals; and cracking down on rogue landlords.

Theresa May’s Conservatives have revealed fewer detailed policies, apart from promising to crack down on rip-off energy bills – a plan proposed by Labour in its 2015 election manifesto, when Ed Miliband was the leader.

But with Labour’s economic competence likely to be a central issue in the campaign, the party will face growing scrutiny of its policy pledges, and how it will make its manifesto add up – particularly since it has opted to guarantee the triple-lock on the basic state pension.

The home secretary, Amber Rudd, said: “Diane Abbott has laid bare the chaos that Britain would face if Jeremy Corbyn is voted into Downing Street.

“One of Corbyn’s closest allies has clearly shown that Labour’s sums don’t add up, they would weaken our defences, and their nonsensical promises aren’t worth the paper they are printed on.”

Labour’s deputy leader, Tom Watson, who has clashed with Corbyn in the past, used a speech to the Usdaw union conference in Blackpool on Tuesday to urge voters to think less about who they want to be prime minister on 9 June and more about electing strong local MPs, saying Labour MPs would put “interests of working people at their heart”.

He added: “We’ve heard a lot of talk about the qualities you need in a prime minister. Theresa May doesn’t think that the ability to answer questions is one of them.

“But sometimes the most important question isn’t what makes the best PM. It’s who makes the best MP.”