In the letter from (see critisism of tactics thread) Phillips mentions the possibility of Rodney joining up with Renown, even though Renown had be told to keep clear unless Bismarck was heavily engaged through fear of another 'Hood disaster. If they had joined up would that combination been enough to disable or sink Bismarck, bearing in mind that in the final event Bismarck concentrated on Rodney as she was regarded as the more potent ship,so perhaps Renown might have been able to use her 15" without too much interference ?
After Bismarck was crippled then Rodney alone could have done the job but the RN also had other cards to play, as there was a squadron of torpedo equipped Swordfish circling Bismarck, just waiting to be given the go ahead to attack. After the torpedoes were all expended Ark Royal could have launched further strikes with Swordfish making divebomber attacks with 500lb bombs.
It is doubtful that Bismarck would have chosen to engage Renown if Rodney rapidly closed the range, while Renown kept her distance.
Additionally, the RN 8in cruisers' fire was also rapidly degrading Bismarck's FC and secondary armament (just as PE's had done to PoW) and the combination of this plus Rodney would have overwhelmed a crippled Bismarck.