A flotilla of Russian warships is passing through the English Channel en route to Syria.
Two British naval ships are shadowing the vessels.
The Ministry of Defence said they would be “man-marked every step of the way” while near UK waters.
A Russian tug, believed to be in convoy with the taskforce, entered the channel first off the coast near Ramsgate.
EU leaders have strongly condemned Russia’s involvement in bombing the Syrian city of Aleppo.
The ships are within international waters but UK Defence Secretary Michael Fallon said the UK would “be watching as part of their steadfast commitment to keep Britain safe”.
The UK’s Type 45 destroyer HMS Duncan, escorted by the Type 23 frigate HMS Richmond, sailed from Portsmouth on Tuesday to track the Kuznetsov group as it headed south from the Norwegian Sea.
The aircraft carrier Admiral Kuznetsov and other Russian naval vessels are believed to be heading to the eastern Mediterranean.
It is the only carrier in the Russian navy and can carry more than 50 aircraft.
Its weapons systems include granit anti-ship cruise missiles.