The sub was being escorted by frigate HMS Kent on Tuesday evening and was expected to pass the Strait of Dover today.
It is understood the Stary Oskol, a Kilo-class submarine capable of carrying cruise missiles and torpedoes, was first detected in the North Sea where Nato forces are monitoring the waters.
The Ministry of Defence said it will continue to be shadowed by the Type 23 Duke class frigate, which had been taking part in commemorations for the Battle of Jutland centenary.
Defence Secretary Michael Fallon said: “This shows that the Navy is maintaining a vigilant watch in international and territorial waters to keep Britain safe and protect us from potential threats.”
HMS Kent’s Commanding Officer, Commander Daniel Thomas, said: “Locating this submarine was a combined effort with Nato allies and shadowing such units is routine activity for the Royal Navy.
“We continue to escort the submarine as it conducts its passage, providing a visible presence.”
The incident is the latest face-off between the British and Russian military following several incursions by aircraft in skies around the UK.
In April 2015 a trawler was dragged violently by its nets while fishing 18 miles off the coast of Northern Ireland, leading to suspicions they had snagged on a Russian submarine.