Asked if he thinks Mr Putin is "bluffing", Lord Dannatt said: "We have highly sophisticated and highly capable conventional weapons.
"If you use some kind of nuclear weapon, yes, we of course, we've got the option of responding to the nuclear weapon, but we have got conventional weapons of huge power that actually could be visited upon you.
"If I was in one of the Black Sea fleet ships at the present moment, I wouldn't go to bed at night in my bunk very calmly at night.
"It's quite possible we could sink the complete fleet if we chose to do so."