I can tell you exactly where it comes from. Back when sugar first became importable into Britain, the Kings and Queens gorged themselves silly on the substance because they could afford it. Unfortunately this lead to their teeth going black (as proved by Elizabeth the 1st, her teeth were rotten and discoloured).
To hide the colour of their teeth, they would talk but cover they're top set of teeth with their lip all the time (As these one's show the most when you're talking). The side effect of talking like this is that you get a posh british accent come out of it.
Nowadays the monarchy doesn't have as much respect by the population. But back then, all the slightly lower people on the ladder, i.e. the lords and ladies, copied the actions, dress and speech of their monarch. This led to the upper classes talking like they do (It must have been very funny for the queen to watch, all the people who couldn't afford as much sugar, with whiter teeth, hiding their teeth too, without realising it). This eventaully filtered down through the classes and was just seen as the posh way to speak.
Today it has just evolved into meaning the manner in which you compose yourself. And us brits (sorry about the patriotism there) are stereotyped as being annoyingly calm in a crisis, so it refers to that too.
p.s, firefly - if you think every saying of word that has 'stiff' in it makes it an innuendo, you need to get out more. Do you think that "it's a hard life" etc. is an innuendo too?