According to the report, the Plymouth-based ship located the Russian submarine on Friday morning and then followed her through the Dover Strait and the rest of the English Channel during the weekend.
"Policing the sea both in home waters and further afield is a core business for the Royal Navy," Commander Tim Berry, the commanding officer of HMS Somerset, was quoted as saying by the report.
"Escorting foreign warships, in this case a Russian submarine, through UK waters is just part of our ongoing effort to protect our island nation," he added.
The Krasnodar entered service with the Russian Naval Forces in 2015 and is the fourth of six 636.3 Project submarines. They feature advanced stealth technology, extended combat range and the ability to strike land, surface and underwater targets.
In mid-April, HMS Sutherland had accompanied a Russian naval group passing through the English Channel.
According to the UK Defense Ministry, the group consisted of the Steregushchiy-class corvettes, Soobrazitelny and Boiky, as well as a support tanker and an oceangoing tug.
In January, Fallon made a disrespectful remark about the Russian Northern Fleet carrier group led by the Admiral Kuznetsov aircraft carrier returning from Syria to its base in northern Russia via the English Channel.
The secretary called it a "ship of shame" and said that the UK would be "man-marking these vessels every step of the way around the UK as part of its steadfast commitment to keep Britain safe."
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