The 30-year-old serviceman was arrested in a pre-planned swoop in Somerset, England, yesterday.
The operation involved searches at a house and wooded area in south Devon.
In the North, officers have also searched a number of properties in Larne, Co Antrim, near the two forest parks where the weapons dumps were discovered earlier this year.
The man, who is believed to be from the North, was detained on suspicion of preparation for acts of terrorism.
While the threat posed by violent dissident republicans in the North has been classified as severe for a number of years, in May the British intelligence services raised the threat level in Great Britain from moderate to substantial.
Two separate hauls of weapons were discovered in Carnfunnock and Capanagh parks within three months of each other.
An armour-piercing improvised rocket and two anti-personnel mines were among the cache recovered at Capanagh in May.
Several pipe bombs, magazines and ammunition for an assault rifle as well as bomb component parts and command wires were also concealed in barrels in purpose-built holes in woodland.
In March, bomb-making items were found at nearby Carnfunnock Country Park.
Police said four barrels were unearthed at Carnfunnock — two barrels were empty but two contained a variety of bomb-making components, including wiring, toggle switches, circuit boards, partially constructed timer power units, ball bearings, and a small quantity of explosives.
Larne is predominantly unionist/loyalist in community make-up, so the discovery of the finds led to some initial speculation that they could be linked to loyalist paramilitaries.
However, after assessing the nature of the weaponry, police concluded they likely belonged to dissident republicans.
Since 2009, dissidents have murdered two soldiers, two policemen, and two prison officers in the North.
A stretch of terraced homes on the Old Glenarm Road in Larne was the focus of the Police Service of Northern Ireland searches yesterday.
There was a major police presence at the scene with army bomb disposal units also in attendance.
Police forensic officers in white suits carried out detailed searches throughout the day.
Scotland Yard said the arrest in Somerset was carried out by officers from the Metropolitan Police Service’s Counter Terrorism Command, supported by local police.
A UK Ministry of Defence spokesman said: “We are aware of a police investigation involving the arrest of a member of the armed forces under the 2000 Terrorism Act and will assist this investigation fully.
“It would be inappropriate to comment further on an ongoing investigation.”