The man was photographed walking past a group of Scouts outside the Houses of Parliament as he wore a large Islamic State in Iraq and Syria (ISIS) flag on his back. He was carrying a small child on his shoulders, who was waving a smaller flag.
Police have been criticised for failing to arrest the man who was seen wandering near the Big Ben draped in the Islamic State flag on Saturday.
"The man was spoken to by officers, with consideration given to relevant legislation, particularly the Public Order Act. The decision was taken by officers at the time that the man was acting within the law. He was not arrested," the statement was quoted as saying by the Guardian.
"Wearing, carrying or displaying of an emblem or flag, by itself, is not an offence unless the way in which, or the circumstance in which, the emblem is worn, carried or displayed is such as to cause reasonable suspicion that the person is a supporter or member of a proscribed organisation," it said.
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The decision not to arrest the man came in for sharp criticism on social media, with some using it to question wider notions of public safety.
Images of the man were reportedly posted on a Korean forum after a tourist spotted him in central London.
The incident comes just days before the capital marks the anniversary of those killed in the 7/7 terror attacks in 2005, and a week after 30 British tourists were killed in the Tunisia beach massacre.