On our way to the workshop, Mirayuki and I talked a bit more.
If our theory is true, then we now have the Regressor working with the Hawksmoor family in secret. Despite investigating that family for so long, the Basilisk Order still hasn't been able to extract much information. As expected, the Hawksmoor family guards their secrets extremely well. And it's not like the Regressor would reveal their identity easily anyway either.
On the other hand, we now have a chicken and egg situation, as a new question popped up inside my mind.
So, what comes first, the chicken or the egg? The Hawksmoor family's demonic experiment or the Regressor's demonization?