Another interesting dimension to this story is the URL that's used for the hoax. Just look at it: http://bouncewith.me.uk/europe/8027043.htm. Clearly, you're not being directed to the BBC News website. But it's important to remember that, on Twitter at least, a good portion of the URLs posted are turned into "short links," which save space. So users rarely look at what they're clicking on anymore -- until they get to the destination. Checking the URL, and whether it redirected to a legit website, may or may not happen.
In this case, thankfully, most users seem to get the fact that the story is a joke, but we do seem to have the ideal forum for a potential War of the Worlds-like event.
http://popwatch.ew.com/popwatch/2009/05/zombie-swine-fl.html