The former foreign secretary called for cuts to “absurdly high” stamp duty and warned of an “oligopoly” of construction companies reducing the supply of new homes by “land-banking”.
Mr Johnson has yet to respond to allegations of Islamophobia resulting from an article a week ago in which he compared Muslim women in face-covering veils to letter-boxes and bank robbers, or to demands for an apology from Theresa May and Conservative chairman Brandon Lewis.
He refused to comment to reporters at his Oxfordshire home after his return from a holiday in Italy, instead emerging from the house to offer them cups of tea.
The Muslim Council of Britain is expected to tell Theresa May on Monday that the investigation launched by the Conservative Party into Mr Johnson must not be a “whitewash”.
In a letter, obtained by The Guardian, the MCB said: “We are hopeful that the party will not allow any whitewashing of this specific inquiry currently in process.
“No-one should be allowed to victimise minorities with impunity.”
The Tell Mama project, which monitors anti-Muslim violence, has reported an increase in incidents of abuse aimed at women wearing the niqab or hijab over the past week.
Mr Johnson was accused of “casual courting of fascism” by a former David Cameron aide, Lord Cooper.
But Brexit-backing MP Jacob Rees-Mogg denounced the investigation launched into Mr Johnson’s remarks as a “show trial”.
And a ComRes poll for the Sunday Express found that 53% of voters believe Mr Johnson should not be disciplined for his comments, against 40% who think he should.
Far-right US activist Steve Bannon, who was in contact with Mr Johnson during his recent visit to the UK, urged him not to “bow at the altar of political correctness” by apologising.
The former aide to Donald Trump told the Sunday Times that Mr Johnson had “nothing to apologise for” and would be “a great prime minister”.
Former first secretary of state Damian Green, who was Mrs May’s de facto deputy, said he feared Mr Johnson was “being turned into a martyr by the alt-Right”, which would be “a disaster for him and the Conservative Party”.
Writing for the Mail on Sunday, he said: “I am particularly concerned by reports that President Trump’s sacked adviser Steve Bannon is forming a Europe-wide far-Right campaign group - and has been in touch with Boris.
“I hope that no Conservative politician, including Boris, is taking advice from him about how the Conservative Party should behave.”
Mr Johnson made no mention at all of the furore in his latest Telegraph column, in which he described the shortage of housing as “the single biggest and most urgent crisis we face”.
Writing as Mrs May launched her plans to tackle homelessness, Mr Johnson warned of a crisis of confidence in capitalism if young people are unable to buy a home.
He called for a cut in stamp duty and the ditching of affordable housing targets.
“This is meant to be Britain, the great home-owning democracy, but we now have lower rates of owner-occupation for the under-40s than France and Germany,” wrote Mr Johnson.
“That is a disgrace. And you cannot expect young people to be automatically sympathetic to capitalism when they find it so tough to acquire capital.”