Killing the Bismarck

Iain Ballantyne’s new book Killing the Bismarck makes a rather controversial claim: As HMS Rodney, HMS King George V, and several attendant cruisers and destroying were pouring shells and torpedoes into Bismarck, the German crew was trying to surrender.  I haven’t read the book, but there’s a summary in Warships: IFR.  I have a bit on the evidentiary claims at Information Dissemination. Since we’ve been talking quite a lot about the laws of war here lately, I thought I’d give this to the crowd.  The facts of the situation:

• Bismarck was not offering coordinated resistance, although her aft two turrets were firing ineffectually.  Bismarck was at this point largely incapable of moving under her own power.
• It was unclear what percentage of the crew might have been willing to surrender, or whether such an order came from a central authority.
• The potential for attack from German submarines and aircraft was very real.
• A boarding operation would have taken time, and left Royal Navy vessels short of fuel and vulnerable to German counter-attack.
• If the attack had been abandoned, it is possible that the Kriegsmarine might have been able to recover and repair Bismarck.

Under these circumstances, what were the responsibilities of the Royal Navy to the German crew?