Johnson also noted that if "a female student turned up at school or at a university lecture looking like a bank robber", he would request that she remove the burqa if she wanted to speak with him.
With no apology forthcoming, founder and president of the Conservative Muslim Forum Lord Sheikh told the BBC the party should take "severe action" against Mr Johnson. Having someone such as Boris Johnson, ridicule women who wear burka undermines the work that we and other organisations are involved in.
Some suspected Johnson's burqa comments were meant to boost his appeal among right-wing members of the party.
A spokesman for the party declined to confirm the investigation.
As with previous annual reports, we have warned that politicians and media outlets must consider their choice of language around high-profile events, as associated media coverage often stimulates public discourse on issues such as terrorism, religious expression, and immigration, which can legitimise racist, xenophobic and Islamophobic prejudice.
The former foreign secretary has faced a storm of criticism, with Theresa May calling on him to apologise.
Shreen Mahmood, a radio presenter in Birmingham who wears the hijab, said she had suffered verbal abuse and knew of others who had been spat at or had their head coverings pulled.
The MCB wrote to Lewis, the Conservative Party Chair, in May to highlight incidents of alleged Islamophobia in the party and to call for an inquiry.
Other than Armeena Khan, the former United Kingdom mayor had received responses from many other personalities including former Attorney General Dominic Grieve, Theresa May, Brandon Lewis and Ruth Davidson.
The Evening Standard is edited by George Osborne, himself a former Conservative MP and Chancellor of the Exchequer, the UK's finance minister under Cameron between 2010 and 2016.
It said Islamophobia was "heavily gendered" with white men carrying out nearly three quarters of verified incidents a year ago, while Muslim women made up more than half of victims.