Air Chief Marshal Stuart Peach says cutting or disrupting the cables could have a "potentially catastrophic" economic effect.
Peach told an audience at the Royal United Services Institute that "along with our Atlantic allies, we have prioritised missions and tasks to protect the sea lines of communication."
In yesterday's speech, Peach said that Russia "in addition to new ships and submarines continues to perfect both unconventional capabilities and information warfare." He said NATO is working "to match and understand Russian fleet modernization."
Earlier this month the Policy Exchange think-tank highlighted how Russia had "easily" severed all digital communications to Crimea during its 2014 invasion of the Black Sea peninsula.