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".
Arjun Tendulkar bowls to Virat Kohli
Snow in Sunny's way: Sunil Gavaskar bumps into England fast bowler John Snow while taking a single in the 1971 Test match. Kohli, who is known for his aggression on the field, advised his batsmen against it at crucial junctures in the match.
Harvard study issues shocking warning for female heart attack victims
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.
‘Superman’ Actress Margot Kidder’s Cause of Death Released
The entertainment site quoted the Park County Coroner as saying that Kidder died from an intentional drug and alcohol overdose. McGuane said she found relief knowing that the truth about her mother's death was finally known to the public.
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".