Thanks to everyone for all these great comments!

So far, the "substitution" theory (like "gee" instead of "Jesus Christ!") sounds most plausible to me.

Mike of NUmbria: thanks, I found those links, too (as a matter of fact, most of the links I found seemed to quote the phrases.org entry). I debated whether to include them (or at least one of them), but the "explanation" seemed a bit weak to me, so I left it.

In case folks are wondering what we're referring to, here 'tis (from http://www.phrases.org.uk/bulletin_board/38/messages/1425.html):

Go to the foot of the stairs

Posted by ESC on December 26, 2004

From one of my newly acquired books:
(well) I'LL GO TO THE FOOT OF OUR STAIRS! - "An old north England expression of surprise or amazement - meaning presumably, 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! Used by Tommy Handley in BBC Radio's ITMA (1940s) and elsewhere. Said to have been used by the entertainer George Formby as 'Eeh, I'll go to the foot of our stairs', as also, 'Eeh, I'll go to our 'ouse (pronounced 'our rouse')' - Robina Hinton, Suffolk . Chris Littlefair gave this variation from the North-East : 'I'll go to the bottom of our garden.'" From "Oops, Pardon Mrs Arden! An Embarrassment of Domestic Catchphrases" by Nigel Rees (Robson Books, London, 2001) Page 99-100.

Submitted by viewers/listeners to Mr. Rees on British TV and radio. The dates are when the informants submitted the information to him.

Again, thanks to all who have contributed!