Johnson wrote in The Daily Telegraph this week that Denmark was wrong to ban the burqa, which conceals the face with a mesh or is worn in conjunction with the niqab - a face veil that leaves only the eyes exposed.
The source said that a number of complaints had been received, and would be considered by an independent panel. On those that wear the burka he appeared to draw comparisons with a female student who turned up to school "looking like a bank robber" - adding they should be asked to remove their face covering.
The Conservative code of conduct says members should "lead by example to encourage and foster respect and tolerance". She said she welcomed an investigation, "but let's not pretend this is an isolated incident". Such full covering clothing has been already banned in France.
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Former Tory chairman Sayeeda Warsi, who has accused Johnson of "dog-whistle" Islamophobia, told Sky News: "Boris knew what he was doing when he made those comments". "People do not want a vision of our country thrust down their throat either by me, by Boris or by anybody else". He has not said sorry. "It is ridiculous that these views are being attacked".
Others have suggested Johnson could be positioning himself as a candidate attractive to anti-immigrant, right-wing, anti-European voters who have previously voted for the United Kingdom Independence Party (UKIP), noting his contact with Steve Bannon, the controversial former adviser to US President Donald Trump.
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It would likely have to impose penalties on USA companies doing business in China to make up the difference. China responded by promising to hit $60 billion worth of USA goods coming into the country with tariffs.
Johnson is known for his bombast, elocution, gaffes and provocative stunts, but even a few fellow Tories said he had gone too far this time.
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Prime minister Theresa May backed calls on Tuesday (7) for Johnson to apologise for the disparaging comments, while he branded his critics "ridiculous". "We have to call it out. If we fail to speak up for liberal values then we're simply yielding ground to reactionaries & extremists".