The Tory caused a "civil war" within the party when he wrote that the Muslim women who wore the veils looked like "mailboxes" or "bank robbers" in a newspaper column.
However, a ComRes poll on The Sunday Express showed support for Johnson.
The sympathy was much higher among the older respondents, with 77% of those over 65 and 63% of 55-64 years of age saying that they should not face discipline, while 62% of 18-24 year olds and 55% of those in the The age group of 25-34 said it should.
The survey also found Theresa May, who criticized Boris's comments, barely above him in popularity, with 26% preferring her as the conservative leader versus 24% for Boris Johnson.
Although Boris said that Britain should not do the same with Denmark and ban the burqa, a debate has erupted over its column.
"The burqa and the niqab are horrible ninja-type tribal garments that are pre-Islamic, not Quranic and, therefore, non-Muslim."
Imam Taj Hargey
The Bishop of the Anglican Church, Michael Nazir-Ali, said he believes that burkas should be banned "for reasons of national security" in an interview with the Mail on Sunday.
The Pakistani-born cleric said: "We have all seen how even male terrorists have escaped arrest by donning a burka and effectively escaping."
"For reasons of national security, there will be places like Parliament or Whitehall or councils and chambers of the council where the burka is not allowed."
A respected British Imam and scholar also got in line.
Imam Taj Hargey, of the Islamic Congregation of Oxford, described the burka as a "horrible tribal dress similar to the ninja".
Writing in The Times, Dr. Hargey said: "The burqa and the niqab are horrible ninja-type tribal garments that are pre-Islamic, not Quranic and, therefore, non-Muslim."
He also said that the burka was "nefarious" and a "fashionable entrance door" for militant Islam.
A niqab is a veil that covers the face but leaves the area around the eyes clear, while a burka is a one-piece veil that can leave a mesh screen over the eyes to see.
Islamic feminists often debate whether the full coverage of the face is a symbol of subjugation or the right of a woman to choose what she wears.