[A.A. Cunningham]

Although there are references to priestly celibacy as far back as the 4th Century, priests have been formally forbidden from marrying since at least the 12th Century across the majority of the Catholic Church.

Bingham is engaging in revisionst history. Although he probably wouldn't be able to comprehend it, he should read the following:

[livius]

Even if some of of them may have been married in the first few centuries, the practice was very restrictive. Just as in the Orthodox Church today, priests were allowed to marry only BEFORE ordination, and were not allowed to remarry after the death of their wives. Bishops could only be monks (that is, never married) or widowers.