Having a sore throat or a runny nose is not being ill. Illness is much more serious.It's not life threatening, but being ill and being productive don't go together. If you're ill, and have something that could easily spread to your colleagues, I'd much rather you stayed at home.
Or, you could come in, make the rest of the office ill, and reduce productivity across the board?
EDIT: I should probably add, this is highly dependant on the kind of work you do.
The incubation period of the common cold is 3-5 days. If everyone who caught a cold had a week off work the UK economy would grind to a halt.