Johnson, who resigned last month over the way May is negotiating Brexit, wrote in The Daily Telegraph this week that Denmark was wrong to ban the burqa, a head-to-toe cloak which conceals the face with a mesh or is worn in conjuction with the niqab - a face veil that leaves only the eyes exposed.
He has faced fierce criticism for comparing women wearing the conservative Islamic dress to letter boxes and bank robbers.
Mohammed Sheikh, founder of the Conservative Muslim Forum, said Johnson's article had been "totally out of order".
Meanwhile, former attorney general Dominic Grieve said he would quit the party if Mr Johnson became leader, while ex-minister Anna Soubry said that "many" One Nation Tories would also leave. May said she agreed with Lewis.
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However, the Pakistani-Canadian actress Armeena, took to Twitter to voice among many others denouncing Johnson for the offensive remarks on burqa and sought an apology over the matter. "What starts as useful targets for "colourful political language" and the odd bit of toxic campaigning ends up in attacks on our streets".
But Conor Burns MP, a vocal supporter of Mr Johnson, said it was "bizarre" for Commissioner Dick to use her position to look into the comments with rising crime in the Capital.
"If you say that it is weird and bullying to expect women to cover their faces, then I totally agree - and I would add that I can find no scriptural authority for the practice in the Koran".
Warsi responded in The Guardian, saying Johnson had used rightwing, "alt-right" language in criticising the appearance of the burqa, which contributes to a view that "Muslim women are fair game". "Boris knew the effect and the impact that this kind of dog-whistle politics would have". "I will defend the basic principle which is the right to choose".