She said that the decision would mean that there was no woman and no representative of Remain in the televised showdown.
And she said that if Mr Johnson and Mr Corbyn refused to debate with her, it suggested that “they are sexist or they are scared or possibly both”.
Her comments came as a YouGov poll found that more than half of voters (53 per cent) believe the Lib Dem leader should be invited to take part in the main leaders’ debates, against just 26 per cent who say she should not face off against Mr Johnson and Mr Corbyn.
Some 73 per cent of Remain voters want her included, but even among Leave voters 38 per cent thought she should be invited, against 40 per cent who said she should not. A majority (63 per cent) of Labour voters wanted the Lib Dem leader included, while Conservative supporters were split 43 to 40 in her favour.
Accusing the two leaders of engaging in an “establishment stitch-up”, she asked: “Why are they so scared of taking on a girly swot?”
Speaking outside parliament, flanked by female Lib Dem MPs and candidates, Ms Swinson said: “The TV debates about who will be the next prime minister of our country cannot and should not exclude the only woman leader who is able to be the next prime minister.
“I stand as a candidate to be prime minister and as the leader of the biggest and strongest party of Remain.
“It is a nonsense to suggest that this should go ahead as Leave versus Leave, with no voice for Remain whatsoever. The voice of the millions of people who voted to Remain, who want to stop Brexit and stay in the European Union, must be heard in those leaders’ debates.
“As Liberal Democrats, we will take any action required to make sure that that voice of Remain is represented in those debates.
“We are taking legal advice and we will pursue legal avenues if ITV do not change their format.
“It is so important that millions of Remainers can make sure their voice is represented, that it is a fair debate between the different options on offer and that girls and women across our country see that women can be political leaders and prime ministers too.”
In a letter to Lib Dem president Sal Brinton, ITV's director of news and current affairs Michael Jermey said he believed the broadcaster's plans "are fair, meet our obligations for due impartiality and serve ITV viewers well".
He pointed out that Ms Swinson is invited to take part in an hour-long interview programme alongside SNP, Brexit Party and Green leaders immediately after the Johnson/Corbyn clash, and that another two-hour debate later in the campaign will feature leaders or senior representatives from seven parties, including the Lib Dems.
"It's been suggested that representation of Jo Swinson in a debate that includes two male politicians is important in terms of inspiring girls and women into leadership roles in the future," said Mr Jermey. "We agree that female role models are important, but our invitations have been issued on the basis of the parties they lead, rather than the personal characteristics of the leaders."
Ms Swinson rejected the argument that the Lib Dems should be excluded because of their poor performance in the 2017 election, when they took less than 8 per cent of the vote.
“We are polling just a small amount behind Labour at the moment,” she said. “We beat both Labour and Conservatives in national elections for the European parliament in May this year.”
And she said that when the Lib Dems were polling at a similar level in 2010, her predecessor Nick Clegg was given a place at the podium in election debates.
“In 2010, when our poll ratings were very similar to the ones we have now, Gordon Brown, David Cameron and Nick Clegg were the leaders in those debates. Nine years on, when we have very similar poll ratings, I should be in those debates with Boris Johnson and Jeremy Corbyn.
“Frankly, if they are refusing to debate me, then it looks like they are sexist or they are scared or possibly both.”
Sky News has proposed a three-way debate between Johnson, Corbyn and Swinson for 28 November.
Ms Swinson immediately accepted the invitation and challenged her rivals to do the same, saying: “I’m in. Will you show up Boris Johnson and Jeremy Corbyn?”
The chief executive of the Electoral Reform Society called on the new speaker of the House of Commons to throw his or her weight behind the creation of a debates commission to take decisions out of the hands of broadcasters and politicians and enshrine multi-party TV debates as part of the electoral framework.
“The debate format cannot be held to ransom by party leaders each time,” said Darren Hughes. “In the present anarchic set-up, so much depends on how broadcasters cut deals with politicians.
“So much of our politics feels broken because it happens behind closed doors, rather than with voters’ input. It’s time for citizens to shape a proper structure for TV debates that will last, and bring these perpetual ‘empty chairing’ rows to an end.”
Responding to Sky's proposed debate format, a Plaid Cymru spokesperson said: “Shutting out the third biggest party – the SNP – is lunacy, but in the last three years, Plaid Cymru’s votes have been an equally crucial factor on key issues in Parliament. To exclude us shows a lack of commitment to properly representing the the parties which will decide the future of the UK.
“We backed Sky News’s campaign for fair and representative TV debates. Now we have the chance to have one, they look set to deliver the complete opposite.”
YouGov questioned 3,479 adults on 4 November
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