Theresa May will declare that the Conservatives can represent the “decent, moderate and patriotic” as she seeks to reassert her authority on Wednesday, a day after Boris Johnson made an overt pitch for the leadership of the party.

The prime minister will try to set out her political values after a testing day in which she conceded that Johnson’s crowd-pleasing pitch to a capacity audience of 1,500 had made her “cross” because of his rejection of her Brexit strategy.

Delegates queued for up to four hours and Brexit-backing MPs turned out in force to hear the former foreign secretary call May’s Chequers deal an “outrage” in a speech that raised the pressure on May to show Conservatives that she has a compelling long-term vision.

The prime minister will use her keynote speech in Birmingham to attack Jeremy Corbyn by arguing that “millions of people who have never supported our party” are appalled by what he “has done to Labour”.

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Appealing for centre ground votes, May will add: “They want to support a party that is decent, moderate and patriotic. One that puts the national interest first, delivers on the issues they care about and is comfortable with modern Britain in all its diversity.”

Drawing upon Corbyn’s “for the many, not the few” slogan, May will conclude by saying that the Conservatives should be: “A party not for the few, not even for the many, but for everyone who is willing to work hard and do their best.”

The prime minister will announce that fuel duty will be frozen for the ninth year in a row in the budget later this month at an estimated cost to the Treasury of £800m, after having considered letting the levy rise with inflation. “Money in the pockets of hardworking people from a Conservative government that is on their side,” May will say.

May is under intense pressure to deliver a confident address after last year’s disaster, where she struggled to get through her speech because of a persistent cough and letters on the backdrop gradually began to fall off.

Earlier, in his only appearance at party conference, Johnson had made a leadership pitch by spelling out his own domestic policy agenda in a 40-minute speech in which he called for a return to optimism and said that the government should tackle the housing crisis.

Johnson said: “If I have a function here today it is to try, with all humility, to put some lead in the collective pencil, to stop what seems to me to be a ridiculous seeping away of our self-belief, and to invite you to feel realistic and justified confidence in what we can do.”

The MP urged the Tories to take the fight to Labour but said they would not succeed by imitating them or “by capering insincerely on Labour turf – we won’t get anywhere by metaphorically acquiring beards and string vests and allotments, but by systematically pointing out the damage they would do.”

He added: “Surely to goodness we can take this Tony Benn tribute act and wallop it for six.”

The former foreign secretary said that the housing crisis was a “massive opportunity” for the Tories even though it has worsened during the party’s eight years in power. “If we rise to the challenge, if we get it right, it is an open goal, because this is one of those critical issues where … the facts of life do always turn out to be Conservative.”

At least fifteen hard Brexit MPs watched Johnson’s speech, with former ministers David Davis, Priti Patel and Iain Duncan Smith all watching from the front row, enough to make the approval of a final Brexit deal by parliament uncertain. Father Stanley and sister Rachel were also in the audience.

Johnson repeated his criticisms of May’s proposals for a post-Brexit Britain, warning that “Chequers is a cheat” and would “escalate the sense of mistrust” people have about politicians. “If we get it wrong – if we bottle Brexit now – believe me, the people of this country will find it hard to forgive,” he said.

“This is not pragmatic, it is not a compromise. It is dangerous and unstable – politically and economically,” Johnson told the ConservativeHome event. “This is not democracy. This is not what we voted for. This is an outrage. This is not taking back control: this is forfeiting control.”

May said she did not watch the speech as it was delivered and said that she was “cross” with Johnson because “he wants to tear up our guarantee to the people of Northern Ireland” because of his refusal to support her Chequers plan, which she says would uphold the soft border in Ireland.

Few believe that Johnson has sufficient support in parliament to unseat May when the Commons returns next week, but the prime minister’s performance on Wednesday will nevertheless be closely scrutinised. Former leader Smith succumbed in October 2003, although the Brexit negotiations are at such a delicate stage that a leadership challenge would represent a significant complication.

The party leadership also went to considerable effort to dilute the impact of Johnson’s speech by unveiling its post-Brexit migration policy, starting with May advocating the plans in morning television interviews and the home secretary, Sajid Javid, giving further details of the tiered immigration system on the conference floor an hour before Johnson spoke.

It requires 48 Conservative MPs writing to Graham Brady, the chairman of the 1922 Committee, to trigger a confidence vote in the prime minister. But Brady told a fringe meeting that people should be cautious about believing what backbench Tories tell the media about what they have done.

“There are instances where I will see a Conservative colleague on the television saying they have written a letter to me when they haven’t. I will see them on the television saying they had withdrawn the letter to me, when they haven’t sent it in the first place. You have to be careful what you believe,” Brady said.