UK Defense Secretary Michael Fallon said on Thursday that the military would watch the vessels "every step of the way".
The aircraft carrier Admiral Kuznetsov and its task group are heading south from the Norwegian Sea toward the North Sea.
The Type 45 destroyer HMS Duncan sailed from Portsmouth to monitor the group.
The Royal Navy regularly shadows ships, and is being supported in this instance by the Royal Air Force.
Meanwhile, the Type 45 destroyer HMS Dragon is due to sail to meet two Russian corvettes travelling toward Britain from the direction of Portugal.