In a letter to be sent to the prime minister, the organisation said that no one should be allowed to “victimise minorities with impunity”.
The row over Mr Johnson’s comments which saw him compare women in burqas and niqabs to “bank robbers” and “letter boxes”, continued on Monday with an ex-Downing St aide accusing him of courting fascism.
Meanwhile, 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.
Miqdaad Versi, assistant secretary general of the MCB, said: “They have to understand the consequences of the actions leaders take in our country.
When our leaders, and our politicians, and senior politicians, for that matter, say things that are clearly going to lead to have real consequences on the street for Muslim women, in a way that was very foreseeable – because many Muslim groups straight after the event said that would happen, and it did – then there is a serious question.”
He added: “There are individuals on the street who heard the exact same terminology that Boris Johnson used and that has been recorded.”
Speaking to the BBC Radio 4 Today programme, Mr Versi went on to argue that Mr Johnson’s are “words that are used by the far right”.
In a letter to the prime minister 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.”
Following complaints into Mr Johnson’s words made in his column for the Daily Telegraph, the party is due to decide whether to appoint a formal investigation panel in accordance with its procedures.
Mr Versi claimed that a failure to do so would mean the party views as trivial, any abuse that women receive on the streets as a result.
Tell Mama, which records hate crimes, said there was a “direct link” between the former foreign minister’s comments and an uptick in incidents targeting women who wear the niqab.
In the week before Mr Johnson’s comments, no incidents targeting women who wear face veils were reported – although there were several involving those wearing headscarves.
But women wearing the niqab – which covers the face and hair, apart from the eyes – were targeted on 8 August in London, followed by another three incidents in London and Luton the next day, and a fourth in the capital on Friday.
Mr Johnson was accused of the “casual courting of fascism” by a former David Cameron aide, Lord Cooper.
A ComRes poll for the Sunday Express found however, that 53 per cent of voters believe Mr Johnson should not be disciplined for his comments, against 40 per cent 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.
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