Retired British couple Jane and Alan Kelvey spoke to BBC's Newsnight after coming into close contact with Russian frigate the Admiral Grigorovich on Tuesday morning.
"They gave out five blasts on their horn, which means, have you seen us?", explained Jane.
"We immediately turned two degrees to port so that they could see we'd made a deliberate change, of course, which meant we had seen them," she added.
The Russian Defence Ministry said the yacht had been on a "dangerous approach" towards the warship, and its crew fired into its path with rifles after making several attempts to contact it over the radio and after launching warning flares.
The Ministry of Defence has described the encounter as an "isolated incident" and not linked to the seizure of a Russian shadow fleet tanker in the Channel on Sunday.
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