He also urged increased spending on the public health service.
"The country will back her because they want to get out, that's what they voted for".
Britain's Brexit chief appealed for Conservative Party unity on Monday, as he warned the European Union that the United Kingdom will leave the bloc without a divorce deal rather than accept one that makes Britain follow too many EU rules.
She added: "It's not just about Brexit, it's about the domestic agenda as well".
"If we are going to spend so much on aid - and there is no doubt that it wins Britain friends and admirers around the world - then let's get value for this country as well", Johnson said. "This is the moment to chuck Chequers".
"This is now about a matter of trust between us - the people - and our political class", he said.
"Do not believe them when they say there is no other plan and no alternative", Johnson told the hundreds of Conservatives who queued to get a seat in the 1,500-seat conference hall.
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.
Ms May has argued the Chequers deal is the only credible plan on the table, but says no deal at all is better than a bad deal.
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She urged all sections of her divided party to "come together" behind her negotiating stance after days of criticism of her Chequers blueprint for Brexit .
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"Am I disappointed (that he didn't declare)?"
"Boris is a great mate of mine, we have a very knockabout friendship, but quite a lot of his ideas, I think, are good headlines but not necessarily good policies".
Johnson suggested the party back one of May's earlier Brexit plans which he accuses her of ditching, and joked about a newspaper report that finance minister Philip Hammond did not think Johnson would become prime minister.
When asked by Andrew whether he would serve as Chairman under a Boris Prime Minister, Mr Lewis said: "There is no vacancy there".
"We believe that we have produced a proposal which can operate within the current framework of technology and administration to deliver a free flowing border with no infrastructure on the island of Ireland within the boundaries of a free trade agreement", Baker told BBC radio.
May's team had hoped the conference would hand her a platform to revitalize a pledge she made when she became prime minister in 2016 to help those people who are "just about managing" and try to steal the initiative from Labour.
Conservative party members queued for two hours on Sunday to see leading Brexiteer Jacob Rees-Mogg denounce May's "Chequers plan" for close economic ties with the European Union, one of half a dozen events he is addressing in Birmingham. Only handfuls turned out to hear ministers' speeches in the main hall.
He added: "The reality is there is one clear plan out there for how to deliver on the referendum that respects what people voted for and delivers for our economy in the United Kingdom - the Chequers plan that we agreed and set out in the white paper does exactly that and I'm confident that the Prime Minister, in Europe over the next month or so, will negotiate a deal which she can bring back to Parliament that will get the support of people across Parliament and deliver for the United Kingdom". So, it is no surprise that we have had a range of different views expressed this week.