Throughout that night, Bismarck was the target of incessant torpedo attacks by the Tribal class destroyers Cossack, Sikh, Maori and Zulu, with the Polish Piorun. Neither side scored a hit but the constant worrying tactics of the British helped wear down the morale of the Germans and deepened the fatigue of an already exhausted crew.
On the morning of Tuesday 27 May 1941 Rodney and King George V drew closer to Bismarck, with their enemy well illuminated by the morning sun in the background. Rodney steered to the north so that her gunfire would work the length of Bismarck, while King George V took the side. They opened fire just before 0900. Bismarck returned fire, but her inability to steer and her list to port severely affected her shooting capacity. Her low speed also made her an easy target and she was soon hit several times, with heavy cruisers Norfolk and Dorsetshire adding their firepower. One salvo destroyed the forward control post, killing most of the senior officers. Within half an hour, Bismarck's guns were all but silent and she was even lower in the water. Rodney now closed to point blank range (approx 3 km) to strike the superstructure while King George V fired from further out.
Bismarck continued to fly its ensign. With no sign of surrender, despite the unequal struggle, the British were loath to leave the Bismarck. Their fuel and shell supplies were low - a demonstration of how difficult it was for a battleship to sink a similar unit in a balanced engagement. However, when it became obvious that their enemy could not reach port, Rodney, King George V and the destroyers were sent home. Norfolk had used its last torpedoes, therefore Dorsetshire launched a torpedo which hit the Bismarck at comparatively short range. Although the battleship's upper works were almost completely destroyed, her engines were still functioning and the hull appeared to be relatively sound; therefore rather than risk her being captured, Captain Lindemann gave the order to scuttle and then abandon ship. Most of the crew went into the water, but few sailors from the lower engine spaces got out alive.