Twenty arrests had been made after hundreds of Sikh protesters clashed with the Metropolitan Police on October 22 during a demonstration against the alleged police brutality on community members in Punjab.
One police officer was taken to hospital with a head injury.
However, there were some reports of the peaceful demonstration turning violent after Met Police officers became heavy-handed with some of the protesters.
"I would like to reassure the Sikh community that no disrespect or offence was intended and apologise for any distress, hurt or offence that has been caused," Commander Mak Chishty, the Met's head of community engagement.
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"An incident occurred where a Met Police officer is seen to take a Nishan Sahib, a sacred flag, from a protester, snap the stick and throw it to the floor. This is deeply disrespectful to the Sikh community and is not acceptable," he said.
It also emerged that police had removed kirpans, a ceremonial knife carried by Sikhs, from two protesters following their arrests against the orders of a senior officer.
"This was against the direction of the senior officer present, who immediately apologised during the protest," Chishty said, adding that officers deployed on future protests involving Sikh demonstrators would be briefed on the significance of the Nishan Sahib and kirpans.
A social media group called #SikhLivesMatter has been created in the UK to draw attention to the "acts of Indian government's atrocities which often go unnoticed in the mainstream media".