Which Bible is used by the Church of England?
American Anglican (not an Episcopalian) checking in…
I’ll guess the “New Revised Standard Version”, unless it’s extremely high church, in which case they might use the original “Revised Standard Version” or maybe even the KJV.
EDIT: I should add that I’m guessing this because I went to an Anglo-Catholic ECUSA chruch for several years and they used the RSV. The rector there was as Anglophile as they come (even pronouncing it “Par-lee-a-ment”), so that’s why I guess the RSV.
I thought the KJV was the ‘common’ one. Never associated it with ‘high’ churches. (Of course, I’m non-religious. I know next to nothing about any version.)
Actually, the more formal reference to the KJV is AV, the Authorized Version. It was the official version of every English speaking denomination other than Catholics up until the late 19th century. At that time with the (then recent) discoveries of many additional texts in the original languages (some older than any previously found), the Anglican communion commissioned revised translations with the British English Revised Version appearing in 1881 and the American Standard Version appearing 1901. The copyright for the ASV was purchased by a consortium of religious educators associated with many of the American churches in 1928. In 1937, they decided for one more update, producing the Revised Standard Version (New Testament, 1946, Old Testament, 1952, Apocrypha, 1957). The RSV had incorporated the efforts of many scholars from many denominations and was no longer the work of a single group, but it was accepted by pretty much all the high church groups.
The KJV was never a “common” translation; it was THE translation. However, from the perspective of (mostly American) religious politics, those groups who opposed the newer translations as “tampering” continued to use the KJV and they are strongly associated, in the U.S., with Fundamentalist Christianity with all the cultural baggage that that might convey.
The New Revised Standard Version is the continuing effort to keep the translations abreast of any new developments in biblical scholarship.
A lot of CofE churchs now use the New International Version, particularly the more evangelical churches.
The Authorised Version is rarely used these days, expect for special services.
This one is also fairly popular 
Though the KJV was always used when I was a lad in actual services. This was in Windsor UK, so maybe being the Royal town they were more high church there than elsewhere.
My sole basis for that comment was that most American high churches use Rite I from the Book of Common Prayer (which is high-falutin’ Elizabethian\Carolingian English), whereas most “low” or “broad” churches use Rite II (which is in “modern” English).