Am I opening a can of worms or just poking a stick in a dead issue that nobody has the slightest interest in? Time alone will tell. The fact remains that there is an expression in the British panoply of oddities that is both obscure and worthy of some debate.
Claims for the geographical origin of the phrase can only be narrowed down as far as the West Midlands and include Manchester and the Black Country …at the same time as crediting its later (and wider) use in Yorkshire.
One authority has it that the phrase could have started in complete obscurity …say just one family, it spread into the community and then common use.
I have personal experience of a phrase of similar obscurity …my ex-wife's mother would often make ribald references to the size of some of the more intimate parts of a persons body as "enough to wallop a dog out of a tripe shop." To the best of my knowledge there is no such thing as a specialist shop that sells mainly tripe (and that is only the beginning of the incongruities in such a short phrase).
One explanation I have come upon has more to do with symbolic verbal imagery than anything else. To "go to the foot of the stairs and touch the newel post" (the post at the bottom end of the banisters) was symbolic of beginning one's rite of passage or ascendancy into maturity and adulthood. To find yourself placed back at the 'foot of the stairs' was to be so astonished that you felt as a child may in the face of overwhelming news or information. As explanations go, it has a faint ring of plausibility about it, but seems a little esoteric
Alternatively, a more prosaic explanations may apply such as the fact that in old slum houses in Manchester (and probably other places), it was common for there to be the entrance to a small cellar at the bottom of the stairs. This was normally a dark and dank place, sometimes used for storing coal. It was also sometimes used as a "sin bin" for naughty children.
So "I'll go to the foot of our stairs" may have originated as an exclamation, because "the foot of the stairs" was the entrance to the darkest and dankest place in the house. This would make it similar to saying "Well, I'll be damned" (an exclamation that is based on something unpleasant).
It's equally possible that this old expression of surprise or amazement could have meant that the short walk to the place mentioned would allow the speaker to recover equanimity. Or perhaps it meant it was time to give up and go to bed!
If you know of other explanations that differ widely from the ones on this page, then email me and I will include them ...we may yet get to the bottom of this!