Sajjad Karim, the party's representative for North-West England, said Johnson's controversial comments had pushed the boundaries of acceptable political debate and as a result the party had to decide what future it wanted to embrace.
Star anchor Kay Burley compared being uncomfortable with the burqa to being "offended" by the burned face of Falklands War hero Simon Weston, and another presenter observed that "unfortunately" many people agreed with the former foreign secretary while interviewing a Muslim politician.
"Any clothing a woman is forced to wear which hides both her beauty and her bruises should be banned and have no place in our liberal, progressive country", she said.
Speaking on the BBC's World At One, the MP for Beaconsfield said: "If he was to become leader of the party, I won't be in it".
British Prime Minister Theresa May backed calls Tuesday for her former foreign minister Boris Johnson to apologize for disparaging comments he made about Muslim women wearing burqas - but he branded his critics "ridiculous".
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Klea Bertakis, a physician and researcher at the University of California, Davis, who studies gender dynamics in health care. They found that 13.3% of female patients seen by a male physician died, compared with 12% of women treated by another woman.
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A majority of adults in the United Kingdom do not believe Boris Johnson's comments describing women who wear burkas as looking like "letter boxes" and "bank robbers" are racist, a poll has suggested.
Writing in the Daily Telegraph on Monday, Britain's one-time top diplomat said women wearing the burqa looked like "letter-boxes" or "bank robbers".
She added while many people have found the comments offensive, he "did not commit a criminal offence". "I will defend the basic principle which is the right to choose".
"I do think that we all have to be very careful about the language and terms we use".
She said: "I know that many people have found this offensive".