This Home Office theory reminds me a lot of The Intiative from Season 4 of Buffy: The Vampire, which was not my favorite season for several reasons. It was a weak storyline and Riley was a dud (I was not sad to see him leave later the next season..
But the purpose of Buffy's The Initiative (at first anyway) was to capture demons, make them impudent so they could not kill humans and release the non-threatening ones back into the public. Eventually, it was found out later the group's lead scientist was making a monster/human hybrid to create the ultimate super soldier who ended up killing her and becoming fascinated with human anatomy and why things the way they are. Like I said, season 4 was my least favorite season..
but I can see Home Office kind of working the same way, minus the demons. They could be trying to harness magic for their own dirty motives, instead of destroying it.