A formal decision to refer the former foreign secretary to an investigatory panel headed by a lawyer is expected this afternoon.
Sources said they were sifting through a considerable volume of complaints from the public about the language used by Mr Johnson.
But party leaders also hope referring the issue to the independent panel will cool the outbreak of Tory infighting that has given Jeremy Corbyn a breather from Labour’s anti-Semitism row.
The party code sets out minimum standards of behaviour. It says elected Tories must lead by example to encourage and foster respect and tolerance and act in a manner which upholds the reputation and values of the party.
In a Daily Telegraph column on Monday, Mr Johnson mocked the appearance of women who choose to wear the burka and niqab, saying they resembled letterboxes and bank robbers.
Met Commissioner Cressida Dick today ruled out a criminal investigation, telling the BBC Asian Network: I spoke last night to my very experienced officers who deal with hate crime… my preliminary view is that what Mr Johnson said would not reach the bar for a criminal offence.
But he could face a Whitehall probe into claims he broke the ministerial code by announcing he was taking up the highly-paid Telegraph column before getting consent.
Conservative MP Anna Soubry said: I hope this will be investigated quickly. Boris Johnson needs to show more respect whether it’s to important rules governing the conduct of former ministers or the choices women make on what to wear.
Mr Spellar said it appeared to be a clear breach of ministerial code which states ministers leaving Cabinet must seek advice from the independent Advisory Committee on Business Appointments before taking up a job.
A source close to Mr Johnson conceded he had written to Acoba only after an announcement that he had taken up the column.
It came as London Labour MP Rupa Huq delivered an impression of him on Channel 4 News, saying: Sorry, I just shagged your wife, I didn’t realise, sorry.