National Action became the first far-right group to be outlawed by the government in December last year, six months after the assassination of lawmaker Jo Cox by a far-right sympathiser.
The suspects are being held "on suspicion of being concerned in the commission, preparation and instigation of acts of terrorism", British police said in a statement.
Authorities said the four suspects arrested on British soil were aged between 22 and 32 and came from Birmingham, Ipswich and Northampton in England and Powys in Wales.
The defence ministry later said that some of the suspects were serving soldiers, but did not reveal how many.
"We can confirm that a number of serving members of the Army have been arrested under the Terrorism Act for being associated with a proscribed far right group," it said in statement.
"These arrests are the consequence of a Home Office Police Force led operation supported by the Army," it added.
One of the soldiers was detained in Cyprus, a defence ministry spokesman confirmed to AFP, and is to be transported to the UK where he will be arrested.
According to a British military source, the suspect is a soldier from the Anglian regiment based at Dhekelia garrison, outside Larnaca in southeast Cyprus.
Cyprus became independent from Britain in 1960, but the former colonial power retains sovereignty over some 99 square kilometres (38 square miles) of the island and has more than 7,000 military personnel stationed at its bases there.
The Anglian regiment has only recently arrived on the island for a tour of duty.
"The arrests were pre-planned and intelligence-led; there was no threat to the public's safety," the British police statement said, adding that raids were also being carried out on "a number of properties".
Cox, an MP from the main opposition Labour party, was shot and stabbed to death in her constituency by far-right nationalist Thomas Mair in June 2016.
Mair shouted "Britain first!" as he killed her.
National Action, which had praised Mair's actions, was banned in December.
At the time, Interior Minister Amber Rudd branded the organisation as "racist, anti-Semitic and homophobic".
Eyewitness? Submit your stories now via social or:
Email: eyewitness@pulse.ng
