Johnson is yet to issue a response.
Baroness Warsi repeated her calls for an investigation into Islamophobia within the Conservative party in a piece in the Guardian, and noted there had been a 26% rise in hate crimes against Muslims previous year, according to figures from monitoring group Tell Mama.
Lord Sheikh, the founder of the Conservative Muslim Forum, said an apology would not be enough and said Mr Johnson should be stripped of the Tory whip.
Conservative peer Sayeeda Warsi, a former party chairwoman, accused Johnson of adopting the "dog-whistle" tactics of right-wing firebrand Steve Bannon, US President Donald Trump's former top aide.
The former foreign secretary will be investigated over whether he has broken the party's code of conduct for comments that were widely criticised by figures, including from his own party, as Islamophobic.
May said his remarks "have clearly caused offense" and agreed with the chairman of her Conservative party, Brandon Lewis, who had asked Johnson to apologize.
But Mr Johnson has far more support among the public - with a Sky poll finding that six out of ten Britons do not think his remarks were racist.
Johnson's words have once again validated the view of those that "other" Muslims.
The burka is a full face covering that is associated with a conservative interpretation of Islam.
In an interview with Daily Telegraph, Johnson said full-face veils should not be banned in Denmark but mentioned he found it "absolutely ridiculous" that women choose to "go around looking like letter boxes".
Mr Johnson branded the burka "oppressive" and said it is "weird and bullying to expect people to cover their faces".
Ms Faifi, who wears niqab, a veil which leaves the eyes uncovered, said she could "empathise" with people who find it hard to connect with women whose full faces they cannot see.
Schools and universities should be able to take the same approach if a student "turns up. looking like a bank robber".