Mr Corbyn claimed a general election could lead to a change on the scale of 1945 or 1979 and warned that things “cannot go on as they were before”.
He told the Pen Green Children’s Centre in Corby that Britain faces even greater problems than crashing out of the EU, and said a Labour government would offer the “real change of direction the country needs”.
Mr Corbyn said: “While Brexit is the framework of the crisis we face, the problems facing our country run much deeper.
“A general election triggered by the Tory Brexit crisis will be a crossroads for our country. It will be a once-in-a-generation chance for a real change of direction, potentially on the scale of 1945 or 1979. Things cannot go on as they were before.”
Last week his plan to be installed as a caretaker prime minister to prevent a no-deal Brexit failed to win the support of Tory Remainers and the Liberal Democrats, who he would need on side to succeed.
Liberal Democrats leader Jo Swinson, following Mr Corbyn's speech, tweeted: "MPs from several parties have said they will not support Jeremy Corbyn as PM, so we know he cannot command support in Parliament.
"If he is unwilling to get behind another candidate, then he risks delivering the no-deal Brexit he claims he wants to stop."
Explaining why Mr Corbyn should be the person to lead a temporary government was Shadow chancellor John McDonnell, who claimed "Jeremy's the only person who could bring the whole of the Labour Party together."
He said: "There'll obviously be some dissent from different political parties and individuals as well but I think the leader of the opposition, the main opposition party, he's the one I think who could bring us together."
He added: "There's a seriousness in Parliament that we've got to prevent a no deal so I think people are now willing to enable a caretaker government under Jeremy and a Labour government to do that."
Mr Corbyn was asked whether he'd be happy to step aside as a leader of a caretaker government and make way for someone else to take charge.
His eventual response was a "no" but the crowd of Labour supporters interrupted the journalist's question by shouting over him and one fan could be heard saying "what a disgrace".
He went on: “However the Brexit crisis is resolved, the country faces a fundamental choice.
“Labour offers the real change of direction the country needs: a radical programme to rebuild and transform communities and public services, invest in the green jobs and high tech industries of the future, and take action to tackle inequality and climate crisis.
“The Tories have lurched to the hard right under Boris Johnson, Britain’s Trump, the fake populist and phoney outsider, funded by the hedge funds and bankers, committed to protecting the vested interests of the richest and the elites, while posing as anti-establishment.”
Mr Corbyn added: “Labour believes the decision on how to resolve the Brexit crisis must go back to the people.
“And if there is a general election this autumn, Labour would commit to holding a public vote, to give voters the final say, with credible options for both sides, including the option to remain.”
Conservative Party chairman James Cleverly said: “Jeremy Corbyn has done all he can to frustrate delivering on the referendum result.
“This is a cynical attempt to seize power by a man who would wreck the economy, is soft on crime and won’t stand up for Britain. All Jeremy Corbyn offers is more dither and delay.
“Only Boris Johnson and the Conservatives can provide the leadership Britain needs and deliver Brexit by October 31, whatever happens.”
Watch Jeremy Corbyn's speech in full: