The investigation comes after a pro-Khalistan rally was held at Trafalgar Square in London in August.
British detectives searched a number of properties on September 18 as part of a West Midlands Counter Terrorism Unit (WMCTU) investigation based on intelligence gathered over a period of time.
"The searches were in connection with allegations of terrorist offences in the UK relating to activity in India, and also fraud offences," Asquith said.
"The investigation is led by WMCTU and is not directed by the UK or Indian government."
Sikhs for Justice (SFJ), a human rights advocacy group with radical leaning, held what it calls a "London Declaration" on an independence referendum for the Indian state of Punjab at Trafalgar Square on August 12.
Asquith said that though people in Britain have a right to protest and to demonstrate their views, provided they act within the law, "should a protest contravene the law, the police have comprehensive powers to deal with activities that spread hate or deliberately raise tensions through violence or public disorder".
"This does not negate the right to peaceful protest," he said
"The use of these powers and the management of demonstrations are an operational matter for the police."
(With inputs from agencies.)