"So you've changed your face again," Churchill says, lest we get confused about basic shit on how this show operates, and the Doctor goes, "Yeah, well, had a bit of work done," which makes no sense either in his context or Winston's, but whatever, and then they (Amy) are so happy to be in the war room they can't stand it, and Winston bitches because he called the Doctor a month ago but he's just now showing up. (This timey-wimey problem of the TARDIS doesn't seem to extend past this episode, if you were wondering; I got really anxious thinking it would happen all season or else I wouldn't mention it.) But why did he call the Doctor? We'll never really know.
Churchill's staff of high-ranking military officials is mostly women and disabled minorities, as was the custom in those days, but that doesn't stop him from getting all up in one lady's grill to ask her what's wrong -- nothing -- and to yell Harkonnenishly in her face, "Action this day, Breen! Action this day!" She smiles at Amy nervously before leaving, again for reasons we may or may not figure out later, and takes off. A dude approaches with a report or whatever, and Churchill finally explains why the Doctor's here. Sort of. Except without the "explaining" part.
"I have something to show you. We stand at a crossroads, Doctor! Quite alone, with our backs to the wall. Invasion is expected daily. So I will grasp with both hands anything that will give us an advantage over the Nazi menace." I mean, I guess we're drawing a connection between the TARDIS and the Ironsides -- yes? -- and just how desperate things got there, for awhile, but again: We do this by making Churchill seem gullible and any-means-necessary, like, if in real life he'd had a TARDIS or a Dalek he would have used it. Which -- again, taking into account my lack of historical knowledge -- seems a bridge too far, considering neither of those things exist and anyway, it's us Americans that proved we can't be trusted with our toys.
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.