The morning of Tuesday, 27 May 1941 brought a heavy grey sky, a rising sea and a tearing wind from the northwest. Because of this northwesterly gale, Admiral Tovey concluded an attack on Bismarck from windward was undesirable. He decided to approach on a northwesterly bearing. Provided the enemy continued steering northward, he would deploy to the south on an opposite course at a range of approximately 15,000 yd (14,000 m). Bismarck was sighted bearing 118° at a distance of 25,000 yd (23,000 m).
Rodney and King George V drew closer to Bismarck in line abreast, their enemy well illuminated by the morning sun in the background. Rodney steered to the east so that her gunfire would work the length of Bismarck, while King George V took the side. They opened fire at 08:47. Bismarck returned fire, but her inability to steer and her list to port severely affected her shooting accuracy. Her low speed of 11 kn (13 mph; 20 km/h) also made her an easy target and she was soon hit several times by the large guns of the British battleships, with the heavy cruisers Norfolk and Dorsetshire adding their firepower later, after Bismarck‘s heavy guns had all been put out of action. One 16-inch (406 mm) salvo from Rodney destroyed the forward control post, killing most of the senior officers, while other salvoes destroyed all four gun turrets. Within 30 minutes, Bismarck‘s guns had all been silenced, and the ship was even lower in the water. Rodney now closed to point-blank range (approximately 3 km (1.9 mi)) to fire into the superstructure while King George V fired from further out; so her fire would strike Bismarck from a more vertical angle and be more likely to penetrate the decks.
Bismarck continued to fly its ensign. The battleship’s upper works were almost completely destroyed and although her engines were still functioning, Bismarck was slowly settling by the stern from uncontrolled flooding with a 20 degree list to port. She no longer had any functioning guns, therefore First Officer Hans Oels ordered the men below decks to abandon ship; he instructed the engine room crews to open the ship’s watertight doors and prepare scuttling charges. Gerhard Junack, the chief engineering officer, primed the charges and ordered the crew to abandon the ship. Junack and his comrades heard the demolition charges detonate as they made their way up through the various levels. Most of the crew went into the water, but few sailors from the lower engine spaces got out alive.
With no sign of surrender, despite the unequal struggle, the British were loath to leave Bismarck. Their fuel and shell supplies were low—a demonstration of how difficult it was for a battleship to sink a similar unit even in an unbalanced 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 her last torpedoes; therefore, Dorsetshire launched three torpedoes at comparatively short range, at least one of which impacted on the super-structure as Bismarck was already largely underwater. Bismarck went under the waves at 10:39 that morning.
Dorsetshire and Maori attempted to rescue survivors, but a U-boat alarm caused them to leave the scene after having rescued only 110 Bismarck sailors, abandoning the majority of Bismarck‘s 2,200-man crew to the mercy of the water. The next morning, U-74, dispatched to try to rescue Bismarck’s logbook (and which heard sinking noises from a distance), picked up three survivors and the German weather ship Sachsenwald picked up two survivors.