In modern London, a band of humans survives a virus outbreak only to be attacked by zombies. The plot of the movie hinges around the humans who try to survive against all odds despite a zombie apocalypse around them. In the end, the movie is about human savagery and what science can do when experimentation goes very, very wrong.
Yes I think 28 days later should be considered a zombie movie because in the movie, a virus breaks out that destroys peoples normal brain and body functions. They are undead, and they try to eat humans that are alive. Because so many of these undead humans are in the movie 28 days later, it can definitely be considered a zombie movie.
But the people suffering from it are definitely not "undead". The condition only effects the living, and during the film many infected are shown to be starving to death. Infected individuals are shown killed during the movie by various gunshot wounds, dismemberment and stabbing, being run over with a vehicle and, notably, being hit with a bag of shopping. "Real" zombies are already 'dead', and thus can (normally) only be stopped by destruction of the brain tissue.