"The ships were escorted by the Royal Navy warship HMS Tyne as part of her UK maritime security role and have now left UK waters."
A naval source said: “It’s not provocative but we are keeping an eye on them.”
The ships are expected to pass through the Channel and head south shortly, possibly to relieve other Russian vessels in the Mediterranean.
Russia’s Northern Fleet said the squadron had passed through the Strait of Dover and were now in the Seine Bay off Normandy to wait for a storm to pass.
"While it is anchored the crew are undertaking a series of exercises on how to tackle infiltrating submarine forces and are training on survival techniques in the case of flooding or fire," the fleet said in a statement, according to the state-run news agency, RIA Novosti.
The convoy includes the Alexander Otrakovsky, an amphibious ship, a tanker and a tug.
Earlier this week, the Northern Fleet said that the ships had left their base in the Arctic port of Severomorsk on November 20, and steamed down the Norwegian seaboard, crossing into the North Sea on Tuesday.
On its way to the Channel, the squadron carried out an exercise to simulate repelling an air attack after it was circled by Nato planes, the fleet added.
Russia has been flexing its muscles in Europe this year as a result of the Ukraine crisis and worsening relations with western states.
The RAF scrambled Typhoon jets to intercept two Russian bombers close to UK airspace at the end of last month shortly after Nato reported an “unusual” increase in Russian military flights in European airspace.
Vladimir Putin, Russia’s president, raised eyebrows when his visit to Brisbane for the G20 summit was accompanied by a Russian naval convoy entering waters off Australia.
Last month, the Swedish Navy said it had detected a foreign submarine – thought by observers to be Russian – in its waters in the Stockholm archipelago.