Shall and Will
From 'Grammar' part of The ABC Of Plain Words by Sir E Gowers (1951)

Twenty pages devoted to this subject in The King's English begin with the following introduction:

It is unfortunate that the idiomatic use, while it comes by nature to southern Englishmen (who will find most of this section superfluous), is so complicated that those who are not to the manner born can hardly acquire it; and for them the section is in danger of being useless. In apology for the length of these remarks it must be said that the short and simple directions often given are worse than useless. The observant reader soon loses faith in them from their constant failure to take him right; and the unobservant is the victim of false security.

The author's view in short amounts to this: that if anyone has been brought up among those who use the right idiom, he has no need of instruction; if he has not, he is incapable of being instructed, because any guidance that is short and clear will mislead him and any that is full and accurate will be incomprehensible to him.

Every English text-book will be found to begin by stating the rule that to express the "plain" future shall is used in the first person and will in the second and third:

I shall go
You will go
He will go

and that if it is a matter not of plain future but of volition, permission or obligation it is the other way round:

I will go (I am determined to go)
You shall go (You must go, or you are permitted to go)
He shall go (He must go, or he is permitted to go)

But the idiom of the Celts is different. They have never recognised "I shall go". For them "I will go" is the plain future. American practice follows the Celtic, and in this matter; as in so many others, the English have taken to imitating the American. If we go by practice rather than by precept, we can no longer say dogmatically that "I will go" for the plain future is wrong. The Commissioner of Police for the Metropolis is reported to have said:

When police manpower shortage is solved we will have an answer to the desperate men now willing to maim and murder. Give policemen houses, and we shall have more recruits.

He uses first will and then shall for the plain future in the first person, showing a fine impartiality. That is typical of present-day practice in England. We can no longer say smugly with Dean Alford:

I never knew an Englishman who misplaced shall and will; I hardly ever have known an Irishman or Scotchman who did not misplace them sometimes.

The Irish and the Scots are having their revenge for our bland assumption that English usage must be "right" and theirs "wrong".

Nevertheless, the rule for the official must be to be orthodox on doubtful points of doctrine, and text-book orthodoxy still prescribes shall with the first person to express the plain future. So we must judge the second thoughts of the Commissioner of Police to have been best.