Some of the sensors were found on the seabed, while several were washed ashore.
The military believes that they were placed to gather information about Britain's four submarines equipped with nuclear warheads.
"There should be no doubt that a war is going on in the Atlantic. This is a cat-and-mouse game that has been going on since the end of the Cold War and is now escalating again," says a high-ranking British military officer to the newspaper.
The newspaper's investigation, which took three months, revealed that unmanned Russian vessels were discovered "lurking beside deep-sea cables".
The government also has "credible intelligence" that superyachts owned by Russian oligarchs may have been used to conduct underwater espionage, according to the newspaper.