Ahlam Saed who had gone into a corner shop in Ealing Common on Saturday to buy some sweets was mocked by the man for her outfit in front of his two children.
"I only wanted to get a packet of Starburst. I walked in and he decided to call me Batman and started singing the theme tune," said Saed, who filmed the incident on her phone.
"I could not ignore him, that's why I decided to get my phone out... I had to stand my ground, I didn't want him to think he could continue hurling abuse," Saed was quoted as saying by the 'Evening Standard'.
The man also makes claims about a Muslim couple with "photos of an ISIS flag" displayed on their house.
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"My kids can't even see your face, who are you? Are you a man or woman?" the man says, adding "This is a Christian country. Christian, western world."
Saed said she became "petrified" as the man grew increasingly irate after she confronted him and called him "ignorant" in response to his "Batman" remark.
Saed who moved to London when she was two, started wearing a face veil about four years ago and is the only person in her family to don it.
"It's getting worse since the Brussels and Paris attacks," she said.