Mr Johnson quit Mrs May's Cabinet in protest against the proposal, which critics argue would leave Britain too closely aligned to EU rules and regulations and fail to deliver on the 2016 vote to leave the European Union.
He said: "The third priority for the upcoming Council is to keep our unity on Brexit, unity amongst member states, unity amongst the institutions, unity against the insane notions of some Tory politicians in the last days".
The BBC's Political Editor Laura Kuenssberg wrote on Twitter: "This is what we would euphemistically call a "wide-ranging speech" - a blatant pitch for leadership by Johnson, right in heart of conference where May meant to be in charge".
May said Johnson's Brexit ideas are unworkable.
But her bid to revitalize her domestic agenda and steal the initiative from the main opposition Labour Party has been overshadowed by the party splits over Brexit.
Ahead of his conference appearance, he was pictured out jogging, in what some interpreted as a "parody" of Mrs May's claim that the "naughtiest" thing she did as a child was to run through a field of wheat.
The problem for Johnson "is that he is becoming a politician who is incredibly well created to win the votes of paid-up members of the Conservative Party and is poorly positioned to win votes of anybody else", agrees the New Statesman's Bush.
At the foot of the stage there was a press scrum, cameras trained on former Brexit ministers David Davis and Steve Baker in the front row - alongside Stanley Johnson who'd come to see his son.
"I believe that we can get a deal", she added.
Johnson did not call Tuesday for May to be replaced, saying she should simply change course.
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"We must on no account follow (Labour leader Jeremy) Corbyn, and start to treat capitalism as a kind of boo word", he will say, according to excerpts of his speech. But undoubtedly the biggest reaction came from his attack on the Prime Minister's Brexit proposals; cheers and enthusiastic clapping as he urged the party to "chuck Chequers".
They spend their holidays hiking, and the prime minister enjoys cooking and reading detective novels.
In remarks that will fuel speculation about Mr Johnson's leadership ambitions, he highlighted a key distinction between himself and Mrs May: "Unlike the Prime Minister, I campaigned for Brexit".
In fact, Johnson's speech had more than a little of an 80s feel, with the MP aping former-PM Margaret Thatcher calling for a home-owning electorate, while attacking Labour for being anti-aspiration and demanding further tax cuts.
Mary Wylie, a local party official from Devon in southwest England, said Johnson's speech expressed "my Conservative philosophy".
"We will never do anything that would undermine the principles of our union - never!
What it says is, if a conflict situation, armed conflict obviously, appears to be arising, the Northern Ireland people themselves will have a referendum", he said.
"You know we, he and I, are all members of the Conservative and Unionist Party".
"Many businesses are sitting on their hands frankly waiting to see what the out turn of this negotiation is before confirming their investment plans", he said.
"But we have been very clear, we have got to deliver a deal for the United Kingdom that's good for our economy, make sure people continue to have the opportunity to have job security and job opportunities for the future and respect that referendum and deliver on getting back control of our border, of our laws, of our money and that's what this package does".