So an update, from here, I'm now halfway through Miracle Day and still have no idea why this is happening and it's all gone a bit distastefully on-the-nose.
It would have been more unusual if the Miracle was an act of kindness rather than crazy-bastard-evil. (Maybe it was and it's been twisted around. But presumably it'll have to be cancelled at the end... right?)
The lots of people "die" bit is something of an issue as well. Someone who can turn that off would be an obvious threat...
Since Miracle Day is deliberately so divorced from Whoniverse connections beyond the main characters that it might be better served by being considered a separate setting, it presumably won't turn out to be Whovian monsters involved.
So who in the Doctor's rogue's gallery would do such a thing?
Cybermen would be my first guess. People have been upgraded, but in a way that stretches resources and forces governments to turn to shifty outside help. If they'd snuck into the Module and discovered conversion chambers I wouldn't have been at all surprised apart from the divorced-from-the-Whoniverse thing. And as noted, the Soulless with their near-faceless masks with a single tear... However, making flesh better is a bit counter to their MO.
The Threshold... have never been on TV. But the ultimate "unfettered corporate greed" human villains would seem to be a logical fit for this, and indeed for lots of other "unfettered corporate greed" stories, so why not bring in a recurring "unfettered corporate greed" antagonist?
My best guess would be the Master. Messing with humanity on a grand scale for some weird convoluted Xanatos plot? Sounds like our boy. He has a history of taking over big shifty companies as well, enabling seemingly-benevolent alien threats, and backing experiments that "change what it means to be human". And immortality is an interest of his. And if this were Doctor Who he'd get to tweak the Doctor's nose about it too. Only the fact that it's not is a point against it.
Anyway, it sounds like a group connected to Jack's past. Of course, he has hundreds of years of "past" to choose from, but let's assume it's stuff covered on-screen, in this series particularly.
The Time Agency? But (1) why?! and (2) they really haven't been discussed in this series, suggesting the non-Who new viewers it's built for would be left behind.
Torchwood? Ooh... that's not bad...
So there's a few ideas.
So here's another. A bit Miracle Day, a bit Army Of Ghosts...
Returning to modern Earth, the Doctor and Emily are surprised to find that last week, one night, everyone on Earth who had died the day before came back to life, apparently unharmed. Why? Perhaps some power needed someone alive... and didn't narrow it down...?