Just to add: if we’re talking about the deuteros here, Luther only ‘removed’ them in the sense that he put them in a separate section called “Apocrypha: These Books Are Not Held Equal to the Scriptures, but Are Useful and Good to Read” (he didn’t even translate them personally: his friends Philipp Melanchthon and Justus Jonas did the job). He personally didn’t chuck them out of the Bible altogether. (The only books he didn’t include were Latin 1 and 2 Esdras, which to be fair while found in copies of the Vulgate wasn’t accepted as canonical by Catholics anyway.)
For English Bibles, Puritans and printers are pretty much the ones to blame for the outright disappearance of the deuteros from Bibles. Most Protestant translations starting from Tyndale up to the KJV followed Luther’s example of placing the ‘Apocrypha’ in a section between the OT and the NT. It was only by the mid-17th century that the section started to disappear in some English Bibles, and only the 18th century onwards that the process became complete.
You had to remember that Protestants themselves don’t agree about the deuteros. While Lutherans held that these books were uninspired, they still valued them as supplements and encouraged their study. The Church of England insisted (and insists) that they be included in any Bible intended for public worship (private Bibles are another matter), and includes passages from them in the lectionary and the liturgy, but at the same time it holds, as per the Thirty-Nine Articles, that “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.” (Note: the Thirty-Nine Articles lists Latin 1-2 Esdras). Puritans were really the ones who were against their inclusion in the Bible at all.
The KJV, as other Protestant Bibles at the time, originally included the Apocrypha in a separate section. (While the KJV was really born because when a new translation was proposed to King James in response to the perceived problems of earlier translations as detected by the Puritan faction of the CofE, and while there were Puritans among the translators, overall the translators were instructed to limit the Puritan influence on this new translation: hence the inclusion of the Apocrypha and the KJV’s choice to retain words like ‘church’, ‘baptize’ or ‘bishop’, to which the Puritans objected.) However, by 1644 - during the Puritan ascendancy - the Long Parliament forbade the reading of the books in church, followed by the 1646 Westminster Confession’s declaration that " the books commonly called Apocrypha, not being of divine inspiration, are no part of the canon of the Scripture, and therefore are of no authority in the Church of God, nor to be any otherwise approved, or made use of, than other human writings."
During the Restoration of the monarchy of the 1660s, Bibles used for public reading in churches contained the ‘Apocrypha’, although at the same time, you had some private Bibles without the Apocrypha section.
It was only after 1769, when the KJV’s text was standardized, that things changed. The technological development of stereotype printing made it possible to produce Bibles in large-print runs at very low unit prices. Printers found out that omitting the Apocrypha section reduced the cost, while having increased market appeal to non-Anglican Protestants. In other words, more profit. It is with the rise of Bible societies that the Apocrypha section finally disappeared in many Bibles. The British and Foreign Bible Society withdrew subsidies for Bible printing and dissemination in 1826, under the following resolution:
“That the funds of the Society be applied to the printing and circulation of the Canonical Books of Scripture, to the exclusion of those books, and parts of books, which are usually termed Apocryphal; and that all copies printed, either entirely or in part, at the expense of the Society; and whether such copies consist of the whole or of any one or more of such books, be invariably issued bound; no other books whatever being bound with them: and further, that all money grants to societies or individuals be made only in conformity with the principle of this regulation.”
The American Bible Society adopted the same resolution. Both societies reversed these policies in the 1960s, but still, you can still feel the effects today in the lack of the deuteros in many non-Catholic Bibles.