A soldier from the British base in Dhekelia was among four men arrested on Tuesday, including suspicion of belonging to a banned far-right group and planning terrorist acts.
The men, aged 22 to 32, were detained on suspicion of being involved in the commission, preparation and instigation of acts of terrorism and of being members of the National Action group.
One was arrested in Cyprus by bases authorities at Dhekelia and flown back to the UK on Tuesday night where he was placed in custody. The bases were unavailable for comment on Wednesday morning.
The neo-Nazi organisation became the first far-right group to be outlawed in Britain last year after the murder of member of parliament Jo Cox, whose killing the group had praised.
The four arrests were made by counter-terrorism officers in the cities of Birmingham, Ipswich and Northampton and in Powys, Wales.
“The arrests were pre-planned and intelligence-led; there was no threat to the public’s safety,” West Midlands Police said.
The Ministry of Defence (MoD) said a number of serving members of the army had been arrested.
“These arrests are the consequence of a Home Office Police Force-led operation supported by the army,” an MoD spokeswoman said. “This is now the subject of a civilian police investigation and it would be inappropriate to comment further.”
Britain is on its second-highest threat level, “severe”, meaning an attack is highly likely. Suspected Islamists have killed 35 people this year in London and Manchester, and a man died in June after a van was driven into worshippers near a London mosque.
Last month, a senior police chief said the number of referrals to the authorities about suspected right-wing extremists had doubled since the murder of Cox, who was killed in June last year by a loner obsessed with Nazis and white supremacist ideology.