Colleagues who lunch: aka don't expect a conversation from me while I'm enjoying my cup-a-soup!

When you have your lunch at your desk, you expect a bit of privacy. It's bad enough that you usually end up answering the phone, colleagues' questions, or responding to e-mails while you burn your mouth on your hot and tasty soup, but why do people expect to talk to them socially? If you wanted a social lunch, you'd go the pub or a cafe, wouldn't you? At work, you just want to get your faced filled and have some time to yourself to surf the internet in the five remaining minutes of your break. Is there a polite way to completely ignore somebody? Or do you just tell them to piss off?