Jo Swinson, the new Lib Dem leader, has again ruled out working with Jeremy Corbyn, branding him a Brexiter who could not be trusted to fight for a second referendum to keep the UK in the EU.

She said her door was open to MPs from other parties who wanted to work towards a second referendum.

But she said the Lib Dems could not join a pact with Labour while Corbyn was leader, even in the event of a hung parliament.

Speaking on BBC Radio 4’s Today programme, Swinson was scathing about Labour’s Brexit approach, even though the party has now said it would support a referendum on any deal put forward.

“There is nothing to suggest Jeremy Corbyn can be trusted on Brexit or that he will campaign to remain. Let’s remember in the last referendum he went on holiday for two weeks in the middle of it. Forgive me for not believing Jeremy Corbyn’s mealy-mouthed words on Brexit. He can barely bring himself to say the words ‘people’s vote’,” she said.

“I’m not supporting Jeremy Corbyn. If we are to have an election I would fight as Lib Dem leader as the party of remain that hasn’t equivocated on this, like Jeremy Corbyn.

“There are plenty of people in the Labour party that I can work with, that I do work with. But Jeremy Corbyn is a Brexiteer. He cannot be trusted on Brexit. That is abundantly clear.

“And to boot he is somebody that is failing to deal with the scourge of antisemitism in his own party.”

Profile Jo Swinson Show Jo Swinson, the new Liberal Democrat leader, is something of a veteran in the party, even in parliament, despite not turning 40 before next year. The party’s deputy leader and foreign affairs spokeswoman was just 25 when, in 2005, she took her home seat of East Dunbartonshire, becoming not just the “baby of the house” – the unofficial title for the youngest MP – but also the first Westminster representative born in the 1980s. She served as a junior minister in the coalition government and was a prominent party member until she – along with many other Lib Dems – lost her seat after the party’s near-wipeout in the 2015 general election. She returned in 2017’s snap election and has become one of the party’s most visible figures, long considered the natural heir to Vince Cable. Swinson has been vocal on a number of issues, including the Lib Dems’ record in coalition with the Conservatives. In September she said the party must “own the failures” of the coalition, citing the “hostile environment”, the bedroom tax and NHS changes as policies she particularly regretted. Swinson said the party had been complicit in inflicting too high a price on the poorest to cut the deficit. “I’m proud of what we achieved, but I’m not naive or blinkered about it,” she told the Lib Dem conference. “If we are to claim the successes of our time in government, we need to own the failures of it too. We lost too many arguments. When they fought dirty, we were too nice.” She has also pushed for a strongly anti-Brexit stance, which helped the Lib Dems reach their best poll ratings since 2010. In announcing her leadership bid Swinson called on remain voters from other parties to make the Lib Dems their permanent home. At the start of the 2019 general election campaign she ruled out doing any deal with Labour which would put Jeremy Corbyn into Downing Street. A mother of two young children, Swinson was inadvertently at the centre of a row last year when it emerged the Conservatives had broken a “pairing” agreement with her while she was on maternity leave to try to swing a crucial Brexit vote. The backlash helped push forward new plans for proxy voting by MPs. Peter Walker Political correspondent Photograph: Graeme Robertson

Swinson said she was talking to some Conservative MPs about the possibility of defecting to her party after recruiting Chuka Umunna from Labour via the Independent group. “Our door is absolutely open to people who share our values,” she said.

Since her election by Lib Dem members on Monday, Swinson has come under fire for her role in the coalition government as a minister voting for austerity measures and bringing in controversial policies such as employment tribunal fees.

Ian Lavery, the Labour party chair, said: “Jo Swinson sat at the top table of the coalition government and voted for vicious attacks on the most vulnerable and tax cuts for the super-rich and big businesses.

“Austerity couldn’t have happened without Liberal Democrats – leading to shocking levels of child poverty, the tripling of tuition fees, a homelessness crisis and rising food bank use. Labour is the only party that can stop the Tories and transform Britain so that it works for the many not the few.”

Swinson said she regretted not winning the battle against employment tribunal fees, saying it had been the wrong policy.

But she defended her record in the coalition under David Cameron, saying: “I think we achieved a lot of good things in government … I’ve also been very frank that in owning the successes we also need to be clear there were mistakes made as well.”