The "grammarian's grammarian," H.W. Fowler, published A
Dictionary of Modern English Usage in 1926. (It is kept up to date with periodic revisions. All page references in this article are to A Dictionary of Modern English Usage, 2nd ed. [Oxford: Oxford University Press, 1965].) This work is considered a standard reference, often used as the arbiter when questions of grammar and usage produce conflicting answers. This book is quite forceful about the silliness of the "rule" that one must not end a sentence with a preposition:
It was once a cherished superstition that prepositions must be kept true to their name and placed before the word they govern in spite of the incurable English instinct for putting them late. . . . The fact is that. . . . even now immense pains are sometimes expended in changing spontaneous into artificial English. . . . Those who lay down the universal principle that final prepositions are 'inelegant' are unconsciously trying to deprive the English language of a valuable idiomatic resource, which has been used freely by all our greatest writers except those whose instinct for English idiom has been overpowered by notions of correctness derived from Latin standards. The legitimacy of the prepositional ending in literary English must be uncompromisingly maintained. . . .
In avoiding the forbidden order, unskillful handlers of words often fall into real blunders. . . . (473-474)
In the same section of the book, Fowler explains that "the 'preposition' is in fact [often] the adverbial particle of a phrasal verb, [and] no choice is open to us; it cannot be wrested from its partner" (475).
Here is what Edward D. Johnson, another modern expert, from this side of the Atlantic, says in The Handbook of Good English (N.Y.: Facts on File Publications, 1982. All page references are to this edition.): "Note that it is permissible to end a sentence with a preposition, despite a durable superstition that it is an error" (283).