I watched this in preparation for going to see 28 Years Later in an actual movie theater. Fortunate, because while I'm sure I watched this back in 2002 when it came out, I remembered nearly nothing except "fast zombies".
Except they are technically not zombies: they have been infected with the "rage virus", thanks to the efforts of some earnest, well-meaning, PETA-style activists who break into a primate lab where it's being studied. One of the mad apes gets out, infects a human, and before you know it, Britain is full of starving, pissed-off, infectious, and doomed humans.
There are a handful of the uninfected. For example, J. Robert Oppenheimer "Jim" (Cillian Murphy) who
wakes up in a hospital bed, where he's (apparently) been comatose while all this was going on. Like
the viewer, he's clueless. But eventually he meets up with a few uninfected folks, and after some
scary encounters, they make for a promised refuge run by the army, and 75% of them succeed. But it's
not all it's cracked up to be.