Video report by ITV News political correspondent Libby Wiener
Jeremy Corbyn has vowed not to "play by the rules" in his first major speech of the election campaign.
The Labour leader denied a Conservative victory is a "foregone conclusion" as he vowed to "change the direction of this election".
Mr Corbyn also hit back at claims he has little chance of becoming prime minister when questioned by ITV News Political Correspondent Libby Wiener on his poor opinion poll ratings at the outset of the campaign.
He said he overcame 200-1 odds on being Labour leader in a response Labour MP Dawn Butler then described as a "mic drop".
The prime minister paused her campaigning on Thursday morning to host the President of the European Parliament, Antonio Tajani, at Downing Street as attention switched to her main rival.
The first full day of the 2017 race also sees the Green Party launch their campaign.
Mr Corbyn used his first official speech in London to vow to fight on behalf of Britain's "true wealth creators" and overturn a "rigged system" which favours the wealthy.
Controversial business figures like Sir Philip Green and Mike Ashley and the chief executives of tax-evading multinationals should be worried about the prospect of a Labour victory, he told a crowd of supporters.
Labour's campaign kicked off with the party far behind Mrs May's Conservatives in opinion polls seven weeks ahead of the vote.
But Mr Corbyn attacked claims the outcome of the election can be predicted.
"Much of the media and establishment are saying this election is a foregone conclusion," he said.
"They think there are rules in politics, which if you don't follow by doffing your cap to powerful people, accepting that things can't really change, then you can't win.
"They say I don't play by the rules - their rules. We can't win, they say, because we don't play their game.
"They're quite right, I don't. And a Labour Government elected on June 8 won't play by their rules."
Mr Corbyn denounced those benefiting from the current system as "wealth extractors" and said it is only to be expected that they will oppose him.
"Of course those people don't want us to win," he said. "Because when we win, it's the people, not the powerful, who win.
"The nurse, the teacher, the small trader, the carer, the builder, the office worker win. We all win."
But he insisted: "Things can and they will change. And Labour in this election will be part of a movement of the British people to make that change."
"Labour is the party that will put the interests of the majority first," Mr Corbyn said.
"That's why we will prove the establishment experts wrong and change the direction of this election - because the British people know that they are the true wealth creators, held back by a system rigged for the wealth extractors."
Mrs May hit back at criticisms she called the election out of self-interest and said it is about is about "strengthening our negotiating hand for Brexit" and "sticking to our plan for a stronger Britain".
She also restated her commitment to cutting annual net migration to a "sustainable" level in the tens of thousands.
Video report by ITV News political correspondent Paul Brand
Questions were raised about whether the commitment would feature in the Conservative manifesto for the upcoming general election, after a Cabinet minister suggested that the issue was "not about numbers" but about ensuring Britain had the skilled workers it needs.
But speaking during an election visit to Enfield, in north London, Mrs May insisted: "We want to see sustainable net migration in this country.
"I believe that sustainable net migration is in the tens of thousands.
"Leaving the European Union enables us to control our borders in relation to people coming from the EU, as well as those who are coming from outside."