The live-fire exercise took place in international waters and lasted for 30 minutes.
The Russian warship requested that the Royal Navy’s HMS Tyne reposition to a safer distance, which it did.
The Russian frigate was also being monitored by a French military aircraft which made radio contact with the warship asking it to clarify its intentions, the has been told.
Verify has analysed flight and ship-tracking data which shows the position of HMS Tyne and several British military aircraft operating in and around the Channel near Plymouth on Monday.
Flight data on ADS-B Exchange indicates at least four Royal Air Force and Royal Navy aircraft were flying off the coast of Dorset mostly above the UK’s territorial waters, including two Eurofighter Typhoons, a Voyager air refuelling tanker and a Super Lynx helicopter.
A French military H160M Guépard helicopter also flew out and over the Channel during the afternoon. It is not clear if this is the aircraft which made contact with the Russian warship.
Data on ship-tracking service MarineTraffic shows HMS Tyne began to broadcast its location about 40 miles off Plymouth at 13:57 BST on Monday. It remained in that location for around two hours before departing at 15:56 to return to Plymouth.
HMS Tyne has been tracking Neustrashimy since at least 16 July when both vessels were also captured in the North Sea about 36 miles miles from the port of Felixstowe in Suffolk on a satellite image.
The incident will be a reminder for the new prime minister of increased Russian naval activity near UK waters in recent months.
Last month, Royal Marine Commandos boarded a Russian “shadow fleet” oil tanker in the English Channel in a six-hour operation which was the first of its kind by UK armed forces.
Also in June, a British couple in international waters in the English Channel came across a Russian warship – Admiral Grigorovich – 23 miles off the Isle of Wight.
The frigate fired warning shots as Jane and Alan Kelvey sailed their yacht on what Russia’s defence ministry said had been a “dangerous approach”. However, the couple said they had not been on a “collision course”.
Russian warships regularly pass through international waters in the Channel, which are separate from UK and French territorial waters.