First of all, the printing press had only been invented in 1450; cf. any encyclopedia) and arrived in England only about 1500. If you're talking about the movement of readable Bibles in ordinary English, you want to research William Tyndale, who was persecuted for translating the Greek New Testament (see also Erasmus) into English circa 1526. Possessing earlier versions was punishable by death, so it's doubtful there was broad circulation.

Tyndale was executed for breaking the vernacular Bible laws in 1535, but his work was incorporated (may be the substantial part of) the King James version of the Bible (see Tadmor, Naomi (2010), The Social Universe of the English Bible: Scripture, Society, and Culture in Early Modern England, Cambridge UP, p. 16, ISBN 978-0-521-76971-6).

So huge attempts were made to keep those English Bibles out of circulation until the King James era. That doesn't mean there weren't any, but they weren't widely available and had to be treated as contraband.

For more on Tyndale, see: Paul Arblaster, Gergely Juhász, Guido Latré (eds.) (2002). Tyndale's Testament. Turnhout: Brepols

There were many controversies about his Bible and its wording, showing that some scholarly people were reading it (see Arblaster, above).

Clergymen were of course trained to read the Bible in Greek, but Tyndale's goal was to make it available to everyone (Donald Coggan (1968). The English Bible. Essex: Longmans, Green & Co. Ltd.)

So...to the Apocrypha. Are you asking whether they were available in Greek? Not widely, that's for sure. They were certainly not available to the common people, who could barely get their hands on an English New Testament.

I don't know much about those two specific books, but Bible scholars and clerics didn't start throwing out much of the received tradition as "apocrypha" until the Reformation. A brief review of literature on this topic shows that scholarly writing on these texts is largely confined to Eastern Europe (specifically Yugoslavia) until recently. Old Slavonic copies of it were available long before English copies were available. In fact, I can't find an earlier English translation than James's in 1924.

Do you know of any earlier translation? I sure can't find any evidence of one. If it wasn't in English, it's likely it had much impact in the Renaissance. It was translated in 1924 from the Greek and Old Slavonic into English and the preface of the book makes it sound as if it's the first translation.

Did you read M.R. James' article from 1924? Based on how poor the manuscript evidence is in the modern era, 'popularity' here is a relative term; relative to class, literacy, wealth.

I can do a little more digging, but I am curious to know what sources suggest it was 'popular' in the late Middle Ages.

I cannot speak to "Questions of Bartholomew."

I can say that the first edition of the King James Bible (which you can read here) had a section labeled "Apocrypha" containing some of the deuterocanonical books (Tobit, Baruch, 1 and 2 Maccabees, the extra bits of Esther and Daniel) and some books the Catholics also consider apocryphal (the Prayer of Manasseh).

Those are all pre-Christian (in content, if not in origin).

Prior to that... Tyndale was late 1500s, but he was drawing from Erasmus and had to leave England to get sources, yes? And even then, he was hung for his trouble, if I got the story right.

The usual pattern (from the Gospel of Thomas to the Apocalypse of Peter) seems to be - Church Fathers wrote about this text in the 200s or 300s - all we knew were their quotations and fragments - then, either in the 1800s or the 1940s, copies were discovered in Egypt/Ethiopia/Jordan.

Some of the more "fun" texts were distributed in the Middle Ages/Early Modern period (thinking of the Infancy Gospel of Thomas, with the little clay birds and all), but at some times and places, it was against the law to have various versions or translations of the Bible (see: Tyndale leaving England; see also: Tyndale swinging at the end of a rope), so finding out who could read what or had which book back in the study can get a little tricky.

You might get some joy from flipping through some copies of Wilhelm Schneemelcher... looking briefly through his first volume of NT Apocrypha, it seems like there was a copy of the Questions of Bartholomew in the Vatican and in Slavonic manuscripts, neither of which would make me terribly hopeful that there'd be a copy floating around England in the time you're looking at.

But again, there might be someone else here who has more specific information on these particular texts.

You might also get more joy by asking at /r/AcademicBiblical/ - this seems like something /u/captainhaddock/ or /u/koine_lingua/ would be able to drop a few pounds of science on.