All you do in the demo is escort this bloke to an Underground Station, help an engineer fix a secure doorway thingy, do a few standard 'go and kill ten zombies' quests, and one where you have to go and find lil' Joey's fake leg, aww... Then you need to go to Covent Garden station but you can't actually get there in the demo, there's just a couple of areas leading up to it.

Check your e-mails to see if you've been invited into the beta Bloo, I'm playing it now, and I seem to have been invited twice, so the Open beta could have started. The beta is basically the full game so don't bother with the demo if you've been invited in.