The aprocypha were included in the 1611 translation because they were considered profitable reading by the Anglican Church, and were included in their scheduled scripture readings. They were not considered to be inspired however.
From the Anglican 39 articles of religion, 1571:
Article VI
Of the sufficiency of the Holy Scripture for Salvation
Holy Scripture containeth all things necessary to salvation: so that whatsoever is not read therein, nor may be proved thereby, is not to be required of any man, that it should be believed as an article of the faith, or be thought requisite or necessary to salvation.
In the name of Holy Scripture, we do understand those Canonical books of the Old and New testament, of whose authority was never any doubt in the Church.
Of the names and number of the Canonical Books.
Genesis.
Exodus.
Leviticus.
Numbers.
Deuteronomy
Joshua.
Judges.
Ruth.
The First Book of Samuel.
The Second Book of Samuel.
The First Book of Kings.
The Second Book of Kings.
The First Book of Chronicles.
The Second Book of Chronicles.
The First Book of Esdras.
The Second Book of Esdras.
The Book of Esther.
The Book of Job.
The Psalms.
The Proverbs.
Ecclesiastes, or the Preacher.
Cantica, or Songs of Solomon.
Four Prophets the Greater.
Twelve Prophets the Less.
All the books of the New Testament, as they are commonly received, we do receive, and account them canonical.
And the other books (as Hierome saith) the Church doth read for example of life and instruction of manners; but yet doth it not apply them to establish any doctrine. Such are these following:
The Third Book of Esdras.
The Fourth Book of Esdras.
The Book of Tobias.
The Book of Judith.
The rest of the Book of Esther.
The Book of Wisdom.
Jesus the Son of Sirach.
Baruch the Prophet.
The Song of the Three Children.
The Story of Susanna.
Of Bel and the Dragon.
The Prayer of Manasses.
The First Book of Maccabees.
The Second Book of Maccabees.
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Again, much ado about nothing.