The Bismarck was only a bit larger than the Hood, but the British freaked out when it launched.
Generally, the British were not especially concerned about Bismarck's design in the pre-war period. They were first informed about Germany's plans to build new battleships in a 1936 note, sent by the German government in accordance with the 1935 Anglo-German Naval Agreement (AGNA). This described the dimensions of the design that was to become Bismarck, albeit with significant falsehoods about her draught and displacement. British analysis of this suggested that the Germans were aiming to build a fast ship, with a top speed of 28-30 knots, with a broad beam for good stability as a gunnery platform. It would have a shallow draught, which would be useful in the Baltic. These factors suggested that the new ships were intended for two roles; countering Russia's Baltic Fleet, and making sorties into the North Atlantic against British trade. The British assumed that the Germans would follow the limitations of the AGNA, as well as the Washington/London naval treaties, and limit the maximum displacement of the ship to 35,000 tons. Based on these figures, the ships would have to make serious compromises on armament or protection; a January 1941 analysis using them suggested that Bismarck would have to have a 9in belt and two inches of deck armour. This would be a threat, as it would be a faster ship with better fire control than many British battleships, but would not be overwhelming.
Over the course of the next few years, evidence began to coalesce that the Germans were cheating. An examination of the Italian cruiser Gorizia in drydock at Gibraltar showed that she displaced 2,000 tons more than her stated displacement. This prompted a check on the displacements of French, Italian and German battleships. A 'block coefficient' could be calculated for British battleships by dividing their displacement by the product of their length, breadth and draught. Assuming that other navies used a similar hull form, the displacement of their battleships could be found using this block coefficient and their dimensions. This analysis suggested that the Germans were cheating by roughly 4,000 tons. Intelligence information from spies and naval attaches indicated similarly. When Bismarck was launched in February 1939, the British vice-consul in Hamburg noted that she had a greater draught than official statements implied - and hence a considerably greater displacement. This did not significantly change the RN's opinions, though. British constructers generally saw their new battleships, of the King George V class as being equivalent to, if not superior to, Bismarck.
Bismarck, even with this underestimation of her capabilities, did represent a significant threat to British convoys. Her high speed and endurance meant that she could evade pursuit for long periods. Her armour and firepower meant that only a battleship or battlecruiser could defeat her. To keep the convoys safe, they would have to be escorted by a British capital ships. This would be difficult to do. At the start of 1941, the RN only had 15 capital ships. One of these was undergoing a significant reconstruction, and five of these were in the Mediterranean, facing down the Italian Navy. There were not enough ships to fully protect all the necessary convoys. Putting all the capital ships available onto convoy duty would also give the Germans freedom of action in other ways - there would be no heavy units protecting the coastal convoys, for example. It would make it difficult to transfer ships to other theatres, either to reinforce the Mediterranean in case of losses, or to the Far East in case of rising tensions with Japan. Hunting her down, meanwhile, would be difficult, as only the RN's three battlecruisers and King George V had the speed necessary to catch her.
These issues were brought into sharp relief by the loss of Hood. Hood's loss revealed the weaknesses of the RN's older ships, which were in the majority. Designed with with the assumptions that pre-dominated during WWI, they had thin deck armour and upper belts. This was advantageous for the short-ranged battles of WWI, but was vulnerable at the longer ranges of WWII. The unmodernised ships of the 'R' and Queen Elizabeth class also had problems fighting at long ranges, as their fire control systems and turrets had not been upgraded to allow them to fight effectively at ranges longer than 15-20,000 yards. As a result, only the King George Vs and Nelsons were capable of fighting her and her sister ship, Tirpitz. This made defeating her a key priority, as otherwise she could inflict more heavy defeats on the Royal Navy. The loss of Hood also made things personal. Hood's size and majesty made her essentially the symbol of the interwar Royal Navy. Her large crew meant that many in the RN knew someone who had served aboard her, or was serving aboard her when she sank. This added extra encouragement to sink her.
Once she sank, the RN was able to reassess what they knew about her and Tirpitz. One of her survivors was brought aboard with her damage-control book, which gave information on her dimensions and armour layout. It showed that the Germans had adopted a WWI-style armour layout, with a thinner, shallower belt combined with a curved deck which gave additional horizontal protection. This was good at preventing shells penetrating the belt at closer ranges, but was vulnerable to 'plunging' fire from long-range. The shallow belt and poor underwater protection made her vulnerable to hits below the waterline, as well as to torpedoes. Her thinner deck, placed low in the ship, could easily be penetrated by bombs. Her broad beam made her a poor seakeeper, and her freeboard was too low. While she was dangerous to the older capital ships, she was considerably inferior to the KGVs and Nelsons.