It is almost certain that the Woman Caught in Adultery section of text did not belong at this point in John’s gospel as it was originally written. Of course, we don’t have the original manuscript of John (probably late 1st century) but we do have early and excellent copies.
Our earliest textual witnesses (P66, P75) from the late 100s or early 200s do not have this section of text at all. Nor is it found in two important manuscripts produced in the early/mid 300s, Sinaiticus and Vaticanus. The first surviving Greek manuscript to contain the narrative is the Latin/Greek diglot Codex Bezae, produced in the 400s or 500s (but displaying a form of text which has affinities with “Western” readings used in the 100s and 200s). Codex Bezae is also the earliest surviving Latin manuscript to contain it.
Hence, the first manuscript to contain this piece of text is from around 400-500 AD, supported by the western church, centred around Rome. So, for example, Leo the Great (bishop of Rome, or Pope, from 440–61), cited the passage in his 62nd Sermon, mentioning that Jesus said “to the adulteress who was brought to him, ‘Neither will I condemn you; go and sin no more.'” In the early 400s, Saint Augustine used the passage extensively, and from his writings, it is also clear that his contemporary Faustus also used it.
There is internal evidence, too, that John 7:53—8:11 is not original to the text. First, the inclusion of these verses breaks the flow of John’s narrative. Reading from John 7:52 to John 8:12 (skipping the debated section) makes perfect sense. Second, the vocabulary used in the story of the adulterous woman is different from what is found in the rest of the Gospel of John. For example, John never refers to “the scribes” anywhere in his book—except in John 8:3. There are thirteen other words in this short section that are found nowhere else in John’s Gospel. Third, the pericope bears no relationship to the ‘signs’ theme which orders the purpose of the book (cf. John 20:30-31) and does not add to the revelation of Jesus as Lord and Son of God. Instead the gracious example of Jesus becomes moral/ethical teaching.
So although this section of John’s gospel is fondly held, it is only really published in our modern bibles because of its (doubtful) inclusion in the King James Version. It ought not to have the authority of Scripture but it deserves to be highly regarded in the same way the Protestant Church regards the Apocrypha– it is to be “read by the church for examples of life and instruction in behaviour, but the church does not use them to establish any doctrine.”