To some extent, they did. On the 21st May 1940, with Bismarck and Prinz Eugen in Bergen preparing for their breakout, the British began planning their response. This involved the use of submarines. The French submarine Minerve, already on patrol off the Norwegian coast, was ordered to shift her patrol zone to cover the exits to the Bergen fjords. The British submarine P.31, in the base at Scapa Flow, was dispatched to patrol to the west of Stadtlandet, in case of any movement to the north. However, neither of these subs would encounter Bismarck. Further south, the RN had established regular submarine patrols in the Bay of Biscay following the fall of France. These were primarily intended to stop German submarines leaving their French bases, and to catch blockade runners trying to sneak in. However, they were also useful for hunting raiders that were trying to return to French ports. To this end, the patrols were strengthened whenever a raider was out. On the 24th May, two more submarines were sent from British bases to join the four already on patrol in the Bay of Biscay. They were on alert for Bismarck, but she would be sunk by British surface ships before she reached their patrol areas. One of the German submarines sent to support Bismarck, U-74, would be attacked unsuccessfully by one of these British subs. Finally, the British often escorted convoys with submarines, to protect them against raiders. HMS Thunderbolt was sent out from Halifax to cover convoys in the Mid-Atlantic, while the Dutch submarine O.23 and HMS Severn covered two separate convoys heading north from Gibraltar. Severn and her sister ship Clyde would later be detached to prevent Bismarck making for the Straits of Gibraltar.

None of these plans involved using the British subs to hunt and chase down Bismarck. This was for the simple reason that they could not. The submarines at the time were slow vessels. They made their best speed on the surface, but the design compromises required to make them able to submerge meant that they were rarely good sea boats on the surface. They were limited in size, which meant that they could not fit the large engines required to make high speeds, and were low to the water so they could not make good headway in heavy seas. The fastest British submarines of this period were the large 'fleet' submarines of the 'River' class, of which Severn and Clyde were members. In their best possible configuration, they could make about 22.5 knots, though a more usual cruising speed was about 17 knots. Most other British submarines were slower than this. Bismarck's cruising speed was 19 knots, and her top speed was 30. In other words, she could easily outrun any sub hunting for her. The only chance a submarine would have of catching her was if Bismarck moved into the area where the sub was already patrolling. This was why the British deployed their subs as they did.