The PKK is banned as a terrorist organisation in Turkey, the US and UK, and has been fighting against the Turkish state since the 1980s for greater rights for the country’s significant Kurdish minority.
Officers are carrying out searches at eight addresses across the capital, including the Kurdish Community Centre in Haringey, as part of the investigation.
The search is expected to last up to a fortnight, with the centre and surrounding area closed to the public in the meantime.
Extra officers will carry out patrols over the coming days, the Met said.
Acting Commander Helen Flanagan, from the Met’s Counter Terrorism Command said the arrests over the “very serious allegations” followed a “significant” investigation.
“This investigation and activity is about protecting all of our communities, but particularly those in our Turkish and Kurdish communities,” she added.
“I would urge anyone who thinks they may have been affected or targeted by those linked to the PKK to get in touch.”