> Ancient Greek or Latin "p" corresponds with English "f"
Similarly, ancient Greek "p" corresponds with modern Greek "f", and ancient Greek "b" corresponds with modern Greek "v".
We may have done it first, but the sound change is pretty common. "B" -> "v" is arguably in process in Spanish. Something similar had already happened in Latin; compare Latin "frater" to English "brother" or Latin "fero" to Greek "phero".