But Corbyn said the debate should not be about Brexit but about the battle between "the Conservatives, the party of privilege and the richest, versus the Labour party, the party that is standing up for working people".
It paves the way for a ballot that could radically change the electoral map less than two years after the United Kingdom last went to the polls.
The Labour leader said he "welcomed" the shock announcement of a vote on June 8 and pledged to offer a "clear and credible" choice to the British people.
If a Labour government were elected on June 8, Corbyn remarked that it "won't play by their rules either".
Under Ed Miliband the party secured 43.7 per cent of the vote in the capital while the Conservatives mustered just 34.9%, helping Labour take a total of seven seats off the LibDems and Tories.
Mr Corbyn promises change after "years of broken promises" on areas such as the NHS and education.
May, who also backed staying in the European Union but has since embraced the notion of life outside the bloc, is pitching her campaign on a promise of stable leadership to deliver a good deal for Britain from exit negotiations with Brussels. Will Labour hold on to the seat?
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Asked if he was the next prime minister, Mr Corbyn said: "If we win the election, yes". That is why SNP MPs refused to vote Theresa May out of office yesterday, and every day that the Tories remain in power 430,000 Scots go without a real living wage, Women Against State Pension Inequality go without the pension that they have worked their whole lives for, and young people have their housing benefit stripped away.
The intention is to tie the hands of europhile Conservative MPs who might challenge her in the months ahead, the tabloid said.
"She wants us to believe that she is a woman of her word".
In a video message to constituents, Mr Woodcock said: "I am intending to seek renomination from my local Labour and Co-operative parties to be their official candidate, but I will not countenance ever voting to make Jeremy Corbyn Britain's Prime Minister".
Shadow Chancellor John McDonnell hinted on Wednesday at a tax rise for people earning more than £70,000, who he said the party considered to be "rich". And for some, the prospect of a snap election has led to them calling time on their Parliamentary careers. "Labour is the party that will put the interests of the majority first".
"I want a Labour government that isn't closing hospitals, that isn't underfunding schools..."
Alex Massie in The Spectator believes the general election will first and foremost be a vote on Scottish independence, saying "May can not win a mandate for herself while then denying a mandate to the party that wins the Scottish portion of this election".