"Two Tu-160 strategic bombers have made a planned flight over the neutral waters of the Barents Sea, the Norwegian Sea, and the North Sea", the Russian Defence Ministry said in a statement.
"At some parts of the flight the Russian strategic bombers were escorted by UK Eurofighter Typhoon fighters", the ministry added.
According to a video captured from the cockpit of a Tu-160, the UK fighters came close to the Russian bombers - at one point the distance between them was about several dozen metres.
The latest development came about after Russian authorities revealed that two Russian Tu-160 bombers had carried out fly-overs along Belarus in a bid to maintain security amid the recent migrant crisis in the region.
At the time, the Russian Foreign Ministry released footage of the 4.5-hour flight, underscoring that the operation was not meant as a target against any foreign nation.