Reuters / Luke MacGregor Grenadier Guards from the British Army parade during the Trooping the Colour ceremony in London.
The UK will send 800 troops to Estonia, which borders Russia, as part of a NATO drive to bolster security along Russia's European border. NATO is a military alliance of European countries, as well as the United States.
The troops will be deployed to Tapa, an army base 100 miles from Russia's border, accompanied with tanks, drones, and unmanned aerial vehicles.
The boosted mission represents an increase of 300 troops on the 500 that Fallon committed in July. France and Denmark will also send troops to other positions near Russia's border.
Military experts in Moscow have described the increasingly tense relationship between Russia and NATO countries as being akin to a new Cold War.
Lt Gen Evgeny Buzhinsky, a former Russian military official who now runs Moscow think tank PIR, told The Telegraph this week: "If we talk about the last Cold War, we are currently somewhere between the erection of the Berlin Wall and the Cuban Missile crisis. In other words, teetering on the brink of war, but without the mechanisms to manage the confrontation."
The UK's move comes after Russian President Vladimir Putin stepped up his country's bombing campaign on Aleppo, a city in civil war-torn Syria.
Putin and Syrian President Bashar al-Assad have "destroyed" the city, a stronghold for rebels against Assad's autocratic regime. They have attracted huge international condemnation for the campaign, particularly for the way military planes have targeted schools and hospitals. It has raised worries that an increasingly aggressive Putin will turn his sights on Europe.
Google Maps
Tapa, Estonia, the army base where British troops will be stationed
On Wednesday, Spain - under international pressure - refused a Russian request for three warships to dock at one of its ports. The ships are reportedly heading to Syria to take part in the Aleppo bombing campaign. The Russian ministry later denied that it had ever intended to refuel in Spain.
Fallon said: "Backed by a rising defence budget this deployment of air, land and sea forces shows that we will continue to play a leading role in NATO, supporting the defence and security of our allies from the north to the south of the alliance."