Furious ministers rounded on Boris Johnson for suggesting the UK could renege on its Brexit agreements over the Irish border, calling it unworkable and criticising the former foreign secretary for denouncing agreements made while he was a cabinet minister.

The Department for Exiting the European Union issued a defiant statement rejecting Johnson’s alternative, laid out in a 4,000-word Telegraph article, saying it was “not a workable or negotiable plan,” less that two days before the start of the Conservative party conference in Birmingham.

Government sources mocked Johnson’s disavowal of the December withdrawal agreement, when he had been part of the cabinet that approved it, dismissing his intervention as “another very lengthy article which doesn’t offer any answers”.

Speaking ahead of the conference, May said the government was on the verge of a Brexit deal, despite admitting after the EU summit in Salzburg that the two sides remained some distance apart on customs and the Northern Irish border. “The right deal is close – and with it the opportunity to make life better for ordinary working people,” she said.

But Johnson continued his public intervention with a series of television interviews – his first since quitting over Chequers – criticising the prime minister, warning May that she risked betraying the wishes of leave voters if she persisted with the Chequers deal but stopping short of calling her to go.

Johnson told the BBC: “If you stick with Chequers, the electorate of this country will look at what we have produced and think how on Earth was that the outcome of voting leave.”

He was then asked if he would challenge for the leadership if he failed to persuade May to change course. “My job is to speak up for what I believe in and the vision that I’ve set out today and I believe in it very, very sincerely. I’m going to keep going for as long as it takes,” he said.

Johnson told Sky News he stood by what he had said in his previous columns when he compared fully veiled Muslim women to “letter boxes” and “bank robbers” and said that people should read his articles in full.

In his article on Friday, Johnson said May should renege on the December agreement, which included the Irish “backstop”, keeping Northern Ireland in the customs union and parts of the single market in order to avoid a hard border.

Johnson said the UK should instead pursue a “super Canada trade deal” aiming for zero tariffs and quotas, with investment in new technology to ease customs at the border.

Chris Heaton-Harris, the Brexit minister, hit back at Johnson on Friday evening, saying: “This is not a workable or negotiable plan for Brexit – as both sides have made clear on several occasions. No deal is available without a guarantee that there would be no hard border in Northern Ireland in any eventuality, the so-called Irish backstop.”

A government source also dismissed Johnson’s criticism of the December agreement. “Boris was a member of the cabinet that agreed the December joint report – and praised the PM for doing so – and was part of the committee that agreed the customs backstop,” the source said.

Johnson is set to attend a rally on the night before May’s conference speech, an appearance likely to dominate any preview of her address. But the prime minister is understood to be determined that cabinet ministers put on a disciplined united front at the conference, which begins this weekend with a string of policy announcements planned.

May said the conference theme was “opportunity” and that the party would set out a vision for a post-Brexit Britain, after a fractious few days where senior Tories have publicly cast doubt on the party’s message after Labour focused on on childcare, high street renewal and housing at its conference.

“We’re now at a crucial moment,” May said. “So at this conference, we will be setting out how we will provide opportunity for all – a stronger, fairer country with real opportunity for people who work hard and do the right thing.

Sajid Javid, the home secretary, considered to be a future leadership contender, intends to give teachers, police officers and other officials a new legal duty to take a “public health” approach to violent crime, supported by a £200m “youth endowment fund” targeted at crime hotspots.

Downing Street also announced May would back a bid to host the 2030 Fifa World Cup in the four nations of the UK and Ireland, saying the joint bid would be a “strong contender”.

May said the decision was spurred by the “excitement of this summer’s World Cup” when England reached the semi-finals in Russia. “The decision on whether to bid is, of course, for the football associations to make. But if they decide to go forward, they can count on this government’s full support,” she said.

Any bid would face opposition from a joint campaign by Argentina, Uruguay and Paraguay, which has already launched a bid with their “believe big” slogan.