Let's head up the apples and pears to meet Professor Edwin Bracewell, head of Project Ironside and pretty much a complete cipher -- even less interesting or meaningful than Winston himself -- and let him stutter a whole lot. Amy gawps at the airplanes in the sky and does her best Donna Noble impression, and then Churchill and Bracewell proudly fire off some kind of space lasers, dropping Krauts out of the air, and there's much hip-hip and cheerio to be had, old chum, and the Doctor's weirded out because he's starting to realize that Churchill really will use absolutely anything at his disposal, including alien tech that none of them realize is alien.
The Doctor gets very aggro and finally they wheel out an olive drab Dalek -- which is pretty sexy in its own right -- who tells the Doctor I am your soldier! The Doctor tells it, essentially, to STFU and stop fooling: "Stop this. Stop now! You know who I am, you always know." (Technically true -- Oncoming Storm and all that -- but really only here, in these words, to justify the absolutely absurd scene coming up.)
Bracewell explains that the creature is "one of [his] Ironsides," and puts the thing through its paces: "You will help the Allied cause in any way that you can?" Yes. "Until the Germans have been utterly smashed? Yes. "And what is your ultimate aim?" To win the war! Well, now I'm convinced. The first one's a little ropey but the other two are so totally Dalek.
Which is what the Doctor is trying to explain to them! But they are not having it! They are not Daleks, what does that word even mean? Ironsides! "Blueprints, statistics, field-tests, photographs. He invented them!" The Doctor screeches about it some more, and they tell him the whole story, about how this "genius" appeared out of nowhere with detailed plans to build hostile alien machines and everybody was so impressed. (Amy's mostly impressed with how the guy's Scottish, but I'm not qualified to respond to that. The only Scottish geniuses I know are dyslexic alcoholics with a weird predilection for surfing and stroking ladies' hair with or without their consent.) What I'm confused by is firstly, why did you even call the Doctor (still, yes) if you're going to listen to him flip out and then look at this sketchy as fuck story where the mad scientist showed up with sentient killing machines out of the blue, and not put those facts together?