The UK may find itself “tipped into a general election” if Andy Burnham replaces Keir Starmer as prime minister, Labour’s former deputy leader Harriet Harman said on Tuesday.

If Burnham replaces Starmer as prime minister in the coming months, he may feel he needs to secure his own mandate, partly because Nigel Farage would accuse him of being a “usurper”, she told an audience at the Hay literary festival.

She said: “There is a scenario in which the new leader, let’s call him Andy Burnham, for example, actually thinks: ‘I need a new mandate,’ rather than just manage the implementation of Keir Starmer’s mandate. And if he were to have a big surge in the polls, he might think that in that case, he should go for a general election.”

“We might find ourselves not only with a new prime minister, but somehow tipped into a new general election,” she added.

If Burnham wins the Makerfield byelection on 18 June, it would pave the way for a leadership challenge in which he would probably be the frontrunner.

“I don’t want to say that a change of leadership is inevitable, and I 100% want Andy Burnham to win in that Makerfield byelection and come down to Westminster. But I don’t want a leadership challenge, and I also don’t want a general election – another general election.

“Stability is such a fusty and unsexy proposition, but actually, I think people just want to get on with their lives, get on with their businesses, get on with things, and chopping and changing looks kind of chaotic at the top,” she said, adding that a newfound stability in British politics was one of the promises of Starmer’s government.

Harman, whom Starmer appointed as an adviser on women and girls after Labour’s disastrous results at this month’s local and devolved elections, said she sometimes wondered if she was “the only person on the planet” in favour of letting a prime minister “crack on with doing it, short of misconduct”.

If Burnham becomes leader, “Farage will be saying: ‘Well yes, the country does want a new prime minister, but they want me, they don’t want Andy Burnham. Nobody’s voted for him, he’s a usurper,’” said Harman.

Burnham may thus call a general election to avoid “what Gordon Brown did, which is despite having a surge in the polls once he’d taken over as prime minister, he didn’t go for a general election, and after that things went downhill for him”. Brown did not call a snap election after succeeding Tony Blair following his resignation in 2007.

Harman was deputy leader under Brown and Ed Miliband, and served stints as interim party leader in 2010 and 2015. She became the longest continuously serving female MP in 2016.

Speaking at a live recording of Sky’s Electoral Dysfunction podcast with Beth Rigby and Ruth Davidson, Harman also said there had been “a lot of talk” about whether Britain was “ungovernable”, which she did not think was true. She said it was a “very tough” job but: “I don’t think it’s impossible to be prime minister.”