HMS Sutherland spotted the ships on Friday morning as they sailed through the North Sea towards the Dover Straits.
The Type 23 frigate will monitor the movements of the Steregushchiy-class corvettes, Soobrazitelny and Boiky, as they pass close to United Kingdom territorial waters today, the navy said.
A navy spokesman said the Russian ships had been joined by a support tanker and an ocean-going tug on Friday afternoon.
It comes at a time of strained relations between the countries,, with Foreign Secretary Boris Johnson criticising Russia for vetoing a UN Security Council resolution on Syria, accusing Moscow of covering up the use of chemical weapons by the Syrian regime.
Defence secretary Sir Michael Fallon said: ‘HMS Sutherland is carefully marking these Russian ships as they pass close to UK waters.
‘The Royal Navy maintains a vigilant watch and is always ready to keep Britain safe.’ The Plymouth-based ship will use radar to track the foreign naval vessels.
“The Royal Navy maintains a vigilant watch and is always ready to keep Britain safe.”
Commander Andrew Canale, commanding officer of HMS Sutherland, said: ‘As one of the Royal Navy’s high readiness units, HMS Sutherland is required to escort warships that approach the UK and this task is considered routine business for us.