The British-English exclamative phrase well, I’ll go to the foot of our stairs, and its variants, are used to express astonishment or incredulity. The reason that this metaphor was chosen is unknown.

The earliest occurrences of this phrase that I have found are as follows, in chronological order:

1-: From Shrimps, a short story set in a “midland city”, by Peter Chamberlain, a Birmingham novelist and short-story writer, published in Under Thirty: An Anthology (London: Rich & Cowan Ltd., [1939]), a collection of short stories “written by their authors before attaining their thirty-first year”, edited by Michael Harrison—the barman also uses the phrase well, I’ll go to our house:

Old Joe paused at the door of one of his favourite ports of call. The music-hall patrons would soon be arriving, but, for the first time, he had a momentary doubt whether they would fancy his shrimps. Hesitating at the entrance to the Smoke Room, he finally went into the Public Bar and ordered a half of mild and bitter.
“What you got in the portmanteau, Joe?” asked Harry, the barman.
“Shrimps,” he replied. “’Ave some? Tanner a go.”
“Sez which!” the barman laughed. “What you got?”
“Shrimps, I say, and shrimps they are and bloody all.”
“What’s the game then?”
“Sellin’ ’em, on course.”
“Straight?”
“Ain’t I a-tellin’ you?”
“But what’s the game then?”
“S’truth, like the young bleeder what takes the oysters, on course.”
“Good Gawd Almighty!” the barman put back his head and laughed again. “Well, I’ll go to our ’ouse! You don’t say? Shrimps! Well, I’ll go to the foot of our stairs. Shrimps, eh? You’ll be death of me, you will straight, Joe! ’Ere, let’s ’ave a dekko.”

2-: From After the Funeral, published in Three TV Plays (London: Jonathan Cape, 1961), by the Welsh-born Liverpudlian screenwriter and playwright Alun Owen (1925-1994):

MORGAN (over-emphatic). I am not! I’m Welsh, and my whole identity is here in Wales.
DAVE (in disgust). Well I’ll go to the foot of our stairs! If you want to kid yourself, son, carry on, but don’t drag the old fella into it.

3-: From I, Said the Sparrow (London: Hutchinson, 1963), by the British-born U.S. novelist, poet, essayist and critic Paul West (1930-2015), who was born in Derbyshire, a county of north-central England:

‘Well, I’ll go to the foot of our stairs.’
‘Goo on, then!’
‘Yer cheeky young articles; gerartonit!’
And usually we went, looking for further targets.
There were lorries which came and took soldiers away to do sandbagging in London. But some stayed. I made them stay.

4-: From The Man who travelled on Motorways (London: John Calder (Publishers) Ltd., 1979), by the Lancashire novelist, short-story writer and playwright Trevor Hoyle (born 1940):

‘This is Saddleworth,’ Gorsey Dene said inconsequentially.
‘Is it really,’ Jay said. ‘Well I never. Would you believe it. I’ll go to the bottom of our stairs.’
‘We didn’t manage to get an hotel after all.’
‘Doesn’t look like it,’ Jay said, opening a new packet of menthol cigarettes. She felt utterly depressed.

5-: From the North Wales Weekly News (Colwyn Bay, Denbighshire, Wales) of Thursday 18^th October 1979:

A LOOK AT WHAT MIGHT HAVE BEEN HAPPENING TO THE BLACKED-OUT CHARACTERS OF ITV’S SOAP OPERAS
Scriptwriter John Bartlett, who jointly owns the Holland Arms, Trofarth, takes a light-hearted, affectionate look at how life is carrying on in television’s most famous street—Coronation Street ¹. Viewers have been deprived of their twice-weekly look at life in the legendary Street since ITV went off the air […].
[…]
(ENA SHARPLES APPROACHES THE BAR)
ENA: I’ll have another of them stouts, please, Mrs. Walker. Put it on the slate, will you?
ANNIE: (LONG SUFFERING SIGH. LOOKS AT MILK BOTTLE AGAIN. IT SHATTERS). Mrs. Sharples, I’m never one to criticise, as you know, but the slate is getting rather full and we are not a registered charity.
ENA: Well, I’ll go to the bottom of our stairs—whatever that means—we’ve kept this place going for nigh on twenty years and this is all the thanks we get.

¹Coronation Street is a television soap opera created in 1960, set in Weatherfield, a fictional town based on Salford, near Manchester, in north-western England—cf. a Lancashire phrase: ‘the full monty’ and meaning and origin of the British phrase ‘big girl’s blouse’.

6-: From Very Interesting . . . But Stupid! A book of catchphrases from the world of entertainment (London: Unwin Paperbacks, 1980), by the Liverpudlian author and broadcaster Nigel Rees (born 1944):

(well) I’ll go to the foot of our stairs! Old northern expression used by Tommy Handley in ITMA ², etc.

² This refers to the Liverpudlian comedian Thomas Reginald ‘Tommy’ Handley (1892-1949) in It’s That Man Again (abbreviated to ITMA), a BBC radio comedy programme which ran from 1939 to 1949.