Is it a particularly British idea that you can have an anti-hero who behaves heroically?
I've been watching the latest seasons of the revived Dr. Who with the quite marvelous Christopher Eccleston and David Tennant, and the realization hit me that Dr. Who might have been so successful over the years not just for the previously terrible special effects and obscure plots that drew in sci-fi fans. Rather, that Dr. Who always does the right thing. Not that he doesn't make mistakes. But when everyone is running away from the source of trouble, Dr. Who always runs towards it. He's not always excited about it. He's often, especially in the recent series, exasperated at always landing in the thick of things. (The current run's plot device is that even when he's trying to take a holiday, he arrives in the middle of incipient disaster a la Quantum Leap.)
The same could be said of Harry Potter. He doesn't run. He hates having to be the Chosen One, the one who gets things done, the appointed enemy of Voldemort. (Do you know that the books are so effective, that I almost typed He-Who-Must-Not-Be-Named?) Harry doesn't want to be a hero, but he rarely shirks from his task. He faces it with grim determination. He explains to those who think it's exciting how terrible it all is. He's so frequently near death, that he has lost his fear of it but not his caution.
Dr. Who is the last of his kind in the current running series. His people, the Time Lords, were all killed in an effort to destroy the Daleks, whose goal is simply the destruction of all other life forms in the universe. Harry Potter is the last of his family (the Dursleys aside). Everyone but Petunia and Dudley who are related to him by blood are dead. He fights Voldemort, whose goal is the destruction of all non-wizards and the domination of the world. The Daleks and Voldemort are both the kind of pure evil that isn't actually found outside fiction. (Most evil in our perception is perpetuated by people who have convinced themselves that are pursuing something good. That's the problem with post-modernism, if you accept that no worldview is deluded, and all are equally valid. I can't agree with that.)
I suppose that's why I watch Dr. Who. The itself can be rather fun, but where else do you find an admirable hero who laughs in the face and death, and sacrifices himself again and again and again? Ditto, Potter. Potter in the last book (no spoilers here) engages in the same set of selfless behavior. Both of them are put in positions where they could make the choice to walk away. They sometimes think about it. They sometimes seem to. But they always come back because if not them, then who?