I'm about 98% sure that Thomas More made inaccurate statements about the status of English Bible translations in his time. The book John Wycliffe and Reform by John Stacey directly addresses this issue (See pp. 73ff). In particular, Stacey provides this information:
"Sir Thomas More, whose interest lay in the permission or refusal of the Church to read translations as much as in the translations themselves, made this not unbiased statement: "For ye shal understande that the great arch heretike Wickliffe, whereas the hole byble was long before his dayes by vertuous and wel lerned men translated into the English tong, and by good and godly people with deucion and sobrenes wel and reverently red, toke upon hym of a malacious purpose to translate it of new."
But More's comments likely are not accurate and "it must be assumed from what he said that English translations were common and popular before Wyclif's time" (Stacey 73).
Stacey also observes that More's comments were challenged in 1719 by John Lewis and they apparently have no basis in fact. He concludes:
"As Margaret Deanesly points out, if orthodox translations had existed on any scale, particularly in the period immediately before Wyclif, the opposition to the translations associated with him would be inexplicable. The evidence all points to the fact that there was no widespread reading of the Scriptures in the vernacular and that when Wyclif deliberately took the step of instigating a translation he was breaking with the general tradition" (Stacey 74).
Of course, this post and the quotes above deal with English renderings of the Bible prior to Wyclif (Wycliffe).