The arrests include people aged between 22 and 35 - of which six were nabbed from northwest England, two from South Wales, one from Wiltshire, and two from West Yorkshire, the Metropolitan Police said.
Eleven properties are being searched across England and Wales as part of the investigation led by Counter Terrorism Policing North East and North West.
The arrests were a result of two separate investigations coordinated across a number of police forces, according to the Met's Neil Basu, senior national coordinator for counter- terrorism policing.
Detective Chief Superintendent Martin Snowden, head of the North East Counter Terrorism Unit, said, "Those who promote extreme right-wing views are looking to divide our communities and spread hatred. This will not be tolerated and those who do so must be brought to justice".
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National Action, an anti-semitic, white supremacist group, was banned as a terrorist organisation in December by the home secretary.
The arrests follow activity earlier this month by the West Midlands counter-terrorism unit, which resulted in three men, including two British soldiers, appearing in court, accused of being members of National Action.