We were taught that, for the first person, 'shall' indicates the simple future while 'will' indicates determination: 'I will continue using "whom", regardless of what others may say.' For the second and third person, it's pretty much the other way round: 'will' indicates the simple future, while 'shall' indicates obligation. ('I won't tidy my room!' 'Oh yes you shall!')

This distinction is allegedly unique to England, possibly to the south of England: even there, I doubt it's adhered to much, except by sticklers. One of the older books on grammar (possibly Fowler's Modern Usage, I'd have to check) had the apocryphal story of the Scotsman who fell in the sea off the English coast, and in fear and desperation shouted 'I will drown, and no one shall save me!': onlookers left him to his fate, regretfully but in accordance with his apparently plainly stated wishes.