I'm not able to delete a single contact or all contacts on the Ubuntu One website.
I have a new computer and want to start with an empty address book on Ubuntu One for several reasons.
The Ubuntu One contacts integration in its current form is going away, and doesn't currently work at all well. I'd recommend removing it from the desktop completely until Q (12.10). You can do that by typing the following in a console:
As to the website issue, I'll have the guys look into it as soon as you file a bug. Please reply with the bug number in a comment.