The Navy reported "unusually high levels" of activity in English Channel and North Sea, as it was preparing to help the NHS and other government departments battle Covid-19.
A "large-scale operation" to shadow the ships as they passed the south coast was completed, with assistance from Nato allies France, Norway Germany and Denmark.
Among the Russian vessels were three Steregushchiy-class corvettes, two Ropucha-class landing ships and two Admiral Grigorovich-class frigates, plus their supporting auxiliary ships and tugs.
The executive officer of HMS Tyne, one of the ships involved in the operation, said it is "essential" the Navy continues to protect the British Isles, even while "the Armed Forces are helping the NHS save lives" in the fight against coronavirus.
Lieutenant Nick Ward added: “This is very much part of routine business for HMS Tyne and represents one of the many roles our patrol vessels perform in support of the Royal Navy’s commitments.
“This is our core business and represents an enduring commitment to uphold the security of the UK.”
Other British ships involved in the "concentrated operation" were the HMS Kent, HMS Sutherland, HMS Argyll, HMS Richmond, HMS Mersey along with RFA Tideforce, RFA Tidespring and HMS Echo.
They were supported by Merlin and Wildcat helicopters of 814 and 815 Naval Air Squadrons.
Portsmouth-based HMS Tyne spent more than a week working in the English Channel, in often challenging seas, keeping a close eye on the Russian vessels as they pass the south coast.
The Devonport-based frigate’s Merlin helicopter carried out a number of intelligence-gathering sorties over the Russian ships as they passed through the Channel.
HMS Sutherland’s Operations Officer, Lieutenant Hannah Lee, said: “Our successful integration into the maritime group proves our ability to adapt to task group operations at short notice.
“Having proved we can work together and contributed once again to NATO operations, we now look to return to UK national tasks in support of the very highest defence priorities.”