It's a form of bowdlerisation...that is, a 'nice' way of saying something that others had already said crudely. For example, 'Crikey!' is nothing more that a polite way of saying 'Christ!' and 'Blimey!' started life as 'God blind me!' I'll leave you to work out the original form of 'I'll go to the foot of our stairs' by giving you the opening of it. 'Well, I'll go to f.....'
With some trepidation, for once I'm not sure I entirely agree with Quizmonster. I think there's more irony here than euphemism. The phrase is more an expression of mock, rather than genuine, amazement or surprise. Thus, for me, the point is that the speaker is taken aback by what's just been said to him, enough to make him go to the foot of his own stairs, but not much further!
I think geofbob (above) is on the right lines. My understanding of it is that the person has just heard an amazing piece of information which is so important that it needs to be communicated immediately to the other people in the household (who happen to be upstairs). Therefore you go tho the foot of the stairs in order to shout it up to the others so that they can hear. An even more exciting bit of news would result in the person rushing up the stairs to tell them. So "I'll go the foot of our stairs" refers to something which is moderately fascinating, but not totally fascinating.