"The Progenitor wouldn't recognize you, would it? It saw you as impure! The DNA is unrecognizable as Dalek!" Got it. So we have that whole recursive thing that Moffat loves so much, and I do too, wherein basically machines have to prove to another machine that they're the same machine, but have to do it by tricking, by information. So the Doctor's testimony, which they pried out of him through dodgy story-logic, was that they are, in fact, Dalek. The Progenitor defines them against the Doctor, same as he does.
They start doing shit, freaking him out. "Withdraw now, Doctor, or the city dies in flames!" And how? They turn on every light in London: "Watch as the humans destroy themselves!" Of all the borrowed halo of this show, its shallow references to the Blitz, I have to say that part scared the shit out of me. You get certain images lodged in your brain, and the blackout is a biggie. Terrifying, honestly. Just a light flicking on.
The War Room goes shit-nuts, of course, and everybody runs around, and the PM chomps his cigar, and much worrying happens, and the German squads are coming, and Amy won't sit still for that, and Churchill has once again lost his pep, and then all of a sudden Amy does her best to act like she's organically coming up with an idea, but she's such a good actor and the lines are so incredibly dense and silly that it just ends up annoying. She talks in ellipses, with an absurd look of self-satisfaction, but doesn't actually say anything, because that's how this episode works. Like a rat hitting the pleasure button over and over and over, having forgotten the simple beauty of using your words to tell a story in any other mode than neener-neener. "Oh! Staring us in the face! A gift! From the Daleks!"
The Doctor yells at the Dalek... This room in their ship is marvelous, by the way: all shiny chrome and a sense of hugeness, while shining floor. You could make a screensaver of the shots in this beautiful room. These Daleks are gorgeous, the thing that's about to happen is phenomenally good-looking even if it's totally trashy, and the place it all takes place is fucking brilliant. When I say I hate everything but Matt and Karen, I should say, "And the set dressers and art designers and other practical/below-the-lines, because they are kick-ass." (And weirdly, always totally smoking hot; I've noticed that for years. Not necessarily the case, here in the US.)
So he yells at them to turn off the lights of London, and threatens them some more, and they're like: "Boom. Stalemate. Get lost, we're done with you." The Doctor hisses and spits and explicitly explains the title of the episode, although we don't know that yet: "Oh, that's it? That's your great victory? You leave?" Yes. You're the only one having this fight. "Extinction is not an option. We shall return to our own time and begin again." He throws a literal screaming fit at them about this, basically ordering them to not do what they've just said they're going to do, and already they have him at an impasse: If they leave, London will already be safe. But he's stuck in the story.