Jeremy Corbyn vowed to "transform" Britain by taking on "the few who run a corrupt system" as he kicked off Labour's election campaign.
The party leader promised to "rebuild" public services and hit out at "tax dodgers, dodgy landlords, bad bosses and big polluters".
In a speech, Mr Corbyn called the 12 December poll a "once-in-a-generation chance to transform our country".
But Prime Minister Boris Johnson blamed Mr Corbyn for the delay to Brexit.
He said he was "incredibly frustrated" that the 31 October deadline had to be extended, but a Conservative election win would remove the "logjam".
Both leaders, and those of other parties, are beginning six weeks of campaigning.
In a speech at Battersea Arts Centre, south London, Mr Corbyn received loud cheers from supporters when he said Labour would launch "the biggest people-powered campaign in history".
Flanked by members of the shadow cabinet, he said: "You know what really scares the elite? What they're actually afraid of is paying their taxes. So in this election they'll fight harder and dirtier than ever before. They'll throw everything at us because they know we're not afraid to take them on.
"So we're going after the tax dodgers. We're going after the dodgy landlords. We're going after the bad bosses. We're going after the big polluters. Because we know whose side we're on."
The December election was called for by the prime minister and is taking place after Mr Corbyn agreed to it, following the EU's decision to delay Brexit.
The Labour leader told the audience that, if elected prime minister, he would "open negotiations with the EU about a sensible relationship with Europe".
This wasn't exactly a pitch for the centre ground by Jeremy Corbyn.
His tone was uncompromising.
It's designed in part - just like in 2017 - to enthuse younger voters and previous non-voters, convincing them that politics can make a difference.
But he is also searching for a message that might appeal beyond Brexit - to potential Labour voters in both Leave and Remain areas.
Labour launched its election campaign in the London seat of Battersea.
It doggedly campaigned here in 2017, and won narrowly - it now leads the Conservatives by just 2,416 votes.
It's a reminder that the party will have to work hard to defend seats - as well as targets held by its opponents.
Mr Corbyn also said: "The prime minister wants you to believe that we're having this election because Brexit is being blocked by an establishment elite.
"People aren't fooled so easily. They know the Conservatives are the establishment elite."
Mr Corbyn also said the NHS was "not for sale" and that any future trade deal with the US should not involve giving American firms greater access to it.
The audience, made up of Labour supporters, then repeatedly chanted: "Not for sale."
Several times he asked the audience: "Whose side are you on?" They replied: "Yours."
Mr Corbyn said the prime minister had thought he was being "smart" in calling for an election in December, and thought that Labour supporters "won't go out to vote".
"Even if the rivers freeze over, we're going out to bring about real change for the many, not the few," he added.
The prime minister visited Addenbooke's Hospital, Cambridge, where he said: "I'm incredibly frustrated that we haven't been able to get Brexit done today. We had a fantastic deal on the table."
He said he would deliver Brexit and "bring the country together", adding: "If you vote for us, and we get our programme through - which we will, because it's oven-ready - then we can be out, at the very latest, by January next year."
Mr Johnson promised to "stimulate the wealth-creating sector" if the Conservatives win the election, saying the contest was not about "background" but a "vision for the country".
Meanwhile, Liberal Democrat leader Jo Swinson has defended her decision to campaign as a "candidate to be prime minister", denying such an outcome is a "fantasy".
She told the BBC the UK was in a "very volatile political situation" and anything could happen on 12 December.
Ms Swinson said the Lib Dems could find "arrangements" with other parties in a "small number of seats" to give an anti-Brexit candidate the best chance of winning.
It could see candidates standing aside in areas where their Remain-supporting rivals have a better chance of winning.
Green Party co-leader Jonathan Bartley has said it is "no secret" that the Greens have been "talking to the Lib Dems and Plaid [Cymru]", but "nothing has been finalised".
As other smaller parties geared up for their election campaigns, the Daily Telegraph reported that the Brexit Party was considering helping the Tories to secure a majority by withdrawing hundreds of its general election candidates.
However, leader Nigel Farage said that was "idle speculation", adding: "I have not spoken to anyone of any seniority in the party [about this]."
What happens next?
- Having been approved by Parliament and received royal assent from the Queen, the early election bill has now become law
- On Monday 4 November, MPs are due to elect a new speaker to replace John Bercow
- Just after midnight on Wednesday, 6 November, Parliament will be shut down or be "dissolved" - meaning every seat in the House of Commons becomes vacant
- The electoral authorities have set a deadline of the end of Tuesday 26 November for people to register to vote.
- The cut-off point to apply for postal votes is the same day, but at 17:00 GMT
Do you have any questions about the launch of Labour's election campaign?
In some cases your question will be published, displaying your name and location as you provide it, unless you state otherwise. Your contact details will never be published. Please ensure you have read the terms and conditions.
Use this form to ask your question:
If you are reading this page and can't see the form you will need to visit the mobile version of the BBC website to submit your question.