Modern Infantry Fighting Vehicles use 20mm to 30mm ammunition and can destroy other IFVs at up to 1500m. High explosive rounds have a lethal area of 30m from the point of impact. Even allowing for the extra penetration of modern munitions, sinking a small to medium sized ship should be possible - eventually. A lot of smaller Royal Navy ships are only armed with a single 30mm cannon.
Don't forget that there's a hell of a lot of flammable material inside a ship, and ships regularly sink due to fire on board even without you pumping the hull full of holes!
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