Steak and kidney pie/pudding is called “Kate and Sidney” pie/pudding in British rhyming slang, and it’s also a partial spoonerism. The term “Kate and Sidney” has been cited in print since at least 1909, when a humorous anecdote was printed in many newspapers.
   
“What’s a cannibal’s favorite meal?”/“Kate and Sidney pie” is a popular riddle.
 
     
Wikipedia: Steak and kidney pie
Steak and kidney pie is a savoury pie that is filled principally with a mixture of diced beef, diced kidney (often of beef, lamb, or pork), fried onion, and brown gravy. Steak and kidney pie is a representative dish of British cuisine.
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Popular culture
Among the various vernacular rhyming slang names for steak and kidney pie are Kate and Sidney pie, snake and kiddy pie, and snake and pygmy pie.
 
17 June 1909, The Courier and Argus (Dundee, Scotland), “Men and Matters,” pg. 8, col. 1:
SOMETHING LIKE THAT—In a village not far from Newcastle a miner’s wife presented him with twins. At the usual time the twins had to be christened, and George, his wife, and his friends proceeded to the church to fix the names on the children. The minister asked the father the names of the twins, and he quite proudly replied—“Steak and Kidney, sor!” “Come come,” replied the minister. “These are odd names for your children!” “What d’ye mean, Geordie?” cried his wife. “It’s Kate and Sidney.” “Aye, it is, sor. As thout it was like summit to eat!” shouted George, promptly.
 
15 July 1909, Stamford (CT) Advocate, pg. 3, col. 5:
Christening the Twins.
In an English village a miner’s wife presented him with twins. At the usual time the twins had to be christened, and George, his wife, and his friends proceeded to the church to fix the names on the children. The minister asked the father the names of the twins, and he quite proudly replied:
 
“Steak and Kidney, sor!”
 
“Come come,” replied the minister. “These are odd names for your children!”
 
“What d’ye mean, Geordie?” cried his wife. “It’s Kate and Sidney.”
 
“Aye, it is, sor. As thout it was like summit to eat!” shouted George, promptly.
 
28 December 1913, Shreveport (LA) Times, “Smiles and Fun From Exchanges,” pg. 4, col. 7:
Paddy one day became the proud father of twins. The christening ceremony arrangements were made and Pat was instructed by his wife, Moya, that the babies’ names were “Kate” and “Sidney.”
 
While making his way to the church, repeating the names “Kate” and “Sidney,” Pat was met by several friends, who wished to drink to the babies’ health. By the time all had paid for a round Pat was a wee bit mixed. He arrived at the church in good time, but when the clergyman asked for the names of the children, Pat replied:
 
‘Steak and Kidney.”
       
Twitter
Angel Dame Lexie Dogstoyevsky OTRB
@Dogstoyevsky
RT @GeorgeTheDuck: @Dogstoyevsky no, what is a nice kate and sidney? // it be steak and kidney pie! (dat be cockey rhyming slang)
10:25 AM - 3 Nov 2009
   
Twitter
David Fung
@DavidthePianist
Had a nice “Kate and Sidney Pudding” (a dyslexic version of a steak and kidney) at one of London’s gastropubs called the Fox and Anchor.
7:41 PM - 5 Aug 2011
 
Google Books 
The Diner’s Dictionary:
Word Origins of Food and Drink
By John Ayto
New York, NY: Oxford University Press
2012
Pg. 192:
Kate and Sidney British rhyming slang (and also a partial spoonerism) for steak and kidney (usually pudding, but also applicable to the pie). It is first known in print from 1914, and the earliest record of steak and kidney itself is only from the 1860s, when Mrs Beeton gave a recipe for the pudding.
 
Anglotopia
BRIT FOOD: TOP 10 CLASSIC BRITISH MEALS TO WARM YOUR SOUL AND FILL YOUR STOMACH
January 15, 2013 By Guest Writer
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STEAK AND KIDNEY PIE
The British love their internal organs, or at least those of oxen, sheep, and pigs. Once eaten as a cheap and filling meal, steak and kidney pie is now a comfort food for many Brits and Anglophiles. Usually consisting of beef, kidneys, onion, and gravy, some recipes liven it up with wine, mushrooms, and puff pastry. Cockney rhyming slang has had fun with this dish, coming up with Kate and Sidney pie, snake and kiddy pie, and snake and pygmy pie.