All right, so I've been avoiding going on about the Doctor/Rose relationship in my rewatch discussions up until now. But really, their relationship is the point of Aliens of London and World War III.
There are two points about their developing relationship brought up in this episode that I really feel need addressing:
(1) The implication that there's already romantic love between them. No one brings the word 'love' into it until the next episode, Dalek (though the questioning whether they have a sexual relationship and their reactions are hilarious). But even so, the Doctor hesitates to aim a missile at her and makes it pretty damn obvious that whether or not he's in love with Rose by this stage, he certainly feels deeply for her. I find this interesting, since we're led to believe that the events of Rose, The End of the World and The Unquiet Dead are the only adventures they've had up until this point. There were, to my knowledge, no off-screen detours between any of these episodes. As such, they've really spent just a few days together. Granted, they've been a few emotionally crazy days. The Doctor showed Rose the end of her world so that she could relate to the most important thing in his life at that stage (being his grief over the Time War). They've saved each other's lives and nearly died multiple times. And now they've had to go through the domestic madness that results from the Doctor missing his mark by 12 months. Of course they've grown closer. But it would seem to me that the writers of the show are in little doubt that the Doctor is already in love with Rose by either these or the following episodes. Isn't it still highly questionable at this stage?
This also brings up my opinion that the Doctor is written as having fallen for Rose romantically long before she falls for him that way. Or, at the very least, he's more likely to actually show signs that he's fallen for her. This provides an interesting contrast with the Ten/Rose relationship in Season 2, where Rose is pretty outwardly honest about being crazy about the Doctor, while the Doctor tends to show how much he's in love with Rose only when she's in huge amounts of danger and isn't there to see the way he's acting. In Season 1, it's implied in World War III that the Doctor's fallen for Rose. It's explicitly stated in Dalek (and even if the Doctor obviously doesn't verbally agree to that statement, his actions leave little question in my mind that it's true). And yet several episodes later in The Doctor Dances, Rose reveals that she doesn't really think of the Doctor that way, and in Boom Town goes off with Mickey even though the Doctor has shown some clear interest in her by that stage. The point at which Rose falls for the Doctor is even more unclear than when he falls for her, really. I think she feels like she has a claim over him from quite early on, but she doesn't seem to have any intention of attempting to exert that claim beyond mild passing jealousy until the end of the season. She's obviously incredibly jealous of Lynda in Parting of the Ways, which makes me believe she does fall in love with the Doctor prior to regeneration, at least. But certainly as early in the season as Aliens of London and WWIII, I don't think there's much evidence to back up an assertion that Rose is already in love with the Doctor that way. As a friend, absolutely, she's mad about him. But she doesn't quite consider him boyfriend material yet. Which brings me to point number two.
(2) Rose's "He's not my boyfriend! He's better than that!" line. This, I believe, is not an empty denial on Rose's part intended to shut Mickey up. At this stage of their relationship, I think this is honestly how Rose views the Doctor. She hasn't really thought of him as boyfriend material, but that doesn't mean she doesn't feel close to him. But beyond that, this line says a lot about Rose's psyche.
Now, one might choose to take the quote as meaning that their relationship is powerful enough that they don't need to have a sexual or even romantic connection. I'm sure that's probably along the lines of what was intended when that was written. I, on the other hand, have always implied from this that at this stage Rose has a very low sense of self-worth when it comes to her relationship with the men in her life. She has no father figure in her life to push her to strive for decent men, and she's seen the parade of men Jackie brings through the house. As a result, I don't think she necessarily expects much for herself even before she really enters the dating fray. Then her most serious relationship was with Jimmy Stone and was the worst life choice she'd ever made. Her relationship with Mickey is one that Rose herself looks down on. Any other relationships she has with men aren't considered to be important enough to mention.
So then along comes the Doctor, who's the best thing that ever happened to her, and who's better in so many ways that any human man Rose has been with. It wouldn't surprise me if she had sorted him in the 'way out of my league' category, because she hadn't quite escaped the view of herself as just a shopgirl from the Council Estates yet. That doesn't mean that she thinks friendship with him is beyond her, or that she isn't willing to have a go at taking the Doctor down a peg when she feels he deserves it. I don't think she sees him as above her in that way. I think she views romantic relationships very differently to others. This seems to me to be backed up by the fact that we don't see Rose set her sights on the Doctor that way until she's proven to him and herself that she can be so much more than she'd settled for being in that life she led before him. I think that, along with deciding she can be better, she also starts considering that she might deserve better.
Or maybe I'm overanalysing now.