In the first policy proposal of her campaign, the former shadow business secretary argued working people "have most to lose" from the UK's historic decision to quit the EU.
Ms Eagle, who is from the left of the party, described herself as a "practical socialist" but one who can lead "with the confidence of the Parliamentary party" behind her.
She said: "I am not here for a Labour Party that just takes part".
"Everything we are proud of, from the NHS to the minimum wage to the equality legislation that has modernised and civilized our society is there because we were in government".
At the launch Eagle said that the country was facing a crisis in the wake of the Brexit vote and needed a strong Labour party that was up to the task.
"Oxford Trades Union Council president Pol o Ceallaigh said: "'Trades Council delegates tonight gave a clear message to all those who are in a position to influence events in the Labour Party.
'I have got life experience and values.
"I'm not a Blairite, I'm not a Brownite, and I'm not a Corbynista".
"I'm a gay woman - I know the difference between hope and fear".
"That is why we are calling on the NEC to do the right thing and ensure that Jeremy is on the ballot". I don't think we have ever had that many entryists, even back in the old heydays of the militants.
Ms Eagle said she was ready to "take on all comers" for the leadership. "I am my own woman - a strong Labour woman", she said.
This meant that 81% of MPs voted against their leader.
Those opposed to Mr Corbyn insist he must obtain the active backing of 20% of MPs and MEPs, which amounts to 51 nominations, to get on the ballot paper. He said legal advice he had received backed this view.
The battle looks increasingly likely to end up in the courts, with Mr Corbyn vowing to fight any exclusion from the ballot paper but the anti-Corbyn camp weighing up a legal challenge if he is allowed to stand without the nominations.
It is also unclear whether Corbyn will appear on the ballot in the new election.
Ms Eagle explained in a statement: "These are dark times for Labour".
Pressed whether she wanted others to stand for the post, Ms Eagle said: "I'll take on all comers".
A senior Labour source told the PoliticsHome website that Mr Smith will announce his candidacy this week.
It is possible that calls will be made at the NEC for it to be delayed until next week, when a meeting had been scheduled to be held.
Labour is set for tumultuous month with the potential to split the party as Angela Eagle, a British Labour Party politician and Member of Parliament (MP) launches a bid to oust Corbyn as leader of the party.
"You would be surprised how much support there is out there from people who feel that I was elected a year ago with a very large majority and a very large mandate", Corbyn said in an interview on the BBC's Andrew Marr Show on Sunday. "What I won't accept is any sordid little fix which is alien to our traditions".