The entire Church Slavonic Bible has not been officially translated into English in a faithful, complete, and ecclesiastically sanctioned form. There are some partial efforts and unofficial translations, but these are either incomplete, privately undertaken, or unendorsed by any canonical Orthodox synod—especially among the Old Rite.
Attempts that exist are typically fragmentary (e.g. Psalter or Gospels only), privately produced (by individuals, not Church bodies), or not true translations from Church Slavonic, but instead adaptations from the Synodal or King James versions.
The closest English equivalents include:
Douay-Rheims Bible. Has the full Deuterocanon and a reverent style. It is based on the Latin Vulgate, which often agrees with the Church Slavonic over the Masoretic text.
Brenton Septuagint + DRB New Testament. A side-by-side of these two gives the closest accessible Orthodox-style English rendering of Scripture.
Orthodox Psalter in English. Some editions (e.g. Holy Transfiguration Monastery) render the Psalms from the LXX, which often aligns with the Slavonic Psalter.