Not Cranmer's translation but Miles Coverdale. It is Miles Coverdale's translation of the Roman Canon in the Anglican Use Divine Worship Book -- isn't that right, Theophane?
Someone earlier seems to have thought that Thomas Cranmer translated the whole Bible, unless I misread the statement. He did not, of course, but translated the Psalms for the vernacular Book of Common Prayer, the third edition of which, 1559, was the "Elizabethan" B.C.P. which Shakespeare heard read from in Holy Trinity Church, as Richmond Noble knew. Scriptural readings except Psalms would be from the Bishops' Bible and Psalms always from the BCP in Cranmer's translation.- Shaksper, Global Electronic Shakespeare Conference
I guess it depends on how much revision took place under Cranmer's supervision. He was in charge of the BCP; perhaps he was the editor and Coverdale the primary author. The BCP was compiled from various sources, including Coverdale's Bible, but a good part of it was written and/or revised by Cranmer.
Actually I was told that the Roman Canon translation used in Rite I of the Book of Divine Worship came from an Old Catholic translation, with the Novus Ordo consecration formula substituted for the original. Apparently this translation was known in Rome and Rome then sent it to the Pastoral Provision office saying something like "use this one". I was led to believe that this was done on its own motion by Rome rather than at the request of the US side, which makes it even more remarkable, given that the year was 1987 or thereabouts.
All of the above is, however, subject to correction by someone (Father Parker certainly) who would actually have been there at the creation (or had a direct line to that person). My source is a very good one but perhaps a little bit secondary in nature.