The British-, Irish- and Australian-English slang phrase to (play) hide the sausage means to have sexual intercourse. In this phrase, the noun sausage denotes the penis.
—American-English synonym: to (play) hide the salami.

The earliest occurrences of the phrase to (play) hide the sausage that I have found are as follows, in chronological order:

1-: From Hide The Sausage (London: Beggars Banquet, Friday 23^rd November 1979), a song written and interpreted by ‘Ivor Biggun’, i.e., the British singer-songwriter Robert Cox (born 1946)—the first stanza and the chorus are as follows:

Well there’s a brand new dance
Everybody’s trying to do
It’s better than the pogo
The shimmy or the boogaloo
You can do it by yourself
But it’s much more fun with two
So come on everybody
Let’s go nuts and screw
And this is just what you do

You’ve got to…

Hide the sausage
Come on and hide the sausage
It’s time to hide the sausage tonight
You’ve got to sink the winkle
It’s really very simple
To straighten out your wrinkle tonight
Come on let’s play mums and dads
The moon is shining bright
Come on everybody and hide the sausage tonight
Get it right out of sight

2-: From The Canberra Times (Canberra, Australian Capital Territory, Australia) of Tuesday 16^th December 1986—the title of the cookbook most probably alludes to the phrase:

The book Let’s Play Hide The Sausage […] has extensive information about the varieties of sausages, what is in them, and how to store, prepare and serve them, how much to use, and how to enjoy them in new ways with imaginative cooking.
[…]
The book can be bought from The Presto Kitchen, Wentworth Street, Greenacre, NSW, 2190.

3-: From St Valentine’s Day: Say it with LOVE, published in the Leicester Mercury (Leicester, Leicestershire, England) of Saturday 14^th February 1987:

BORRENCE. Let’s hide the sausage!—Beached Whale. xxx.

4-: From the review of The Sum Of Us, a play by the Australian playwright, screenwriter and director David Stevens (1940-2018)—review by Frank Walker, published in The Sun-Herald (Sydney, New South Wales, Australia) of Sunday 4^th November 1990:

AUSTRALIAN accents haven’t been heard on the New York stage for many moons. Even ex-pat Peter Allen sings I Still Call Australia Home in a broad Yankee drawl.
But a new play set in Melbourne’s Footscray and speckled with Australian slang such as “playing hide the sausage” has New York audiences rolling in the aisles.

5-: From the review of Tonight With Jonathan Ross, which had been broadcast on Channel 4—review by Mark Steyn, published in the Evening Standard (London, England) of Thursday 19^th December 1991:

Introducing a sneak preview of the new Gold Blend ad—a commercial for the commercial—our host wondered, “Does he finally get to play Hide The Sausage?” Doubtless another custom dating back to Roman times, but never very likely to be observed here.

6-: From You’ve no taste Jonathan, a television review by Lynda Gilby, published in the Sunday Life (Belfast, County Antrim, Northern Ireland) of Sunday 22^nd December 1991:

If Wednesday’s Tonight With Jonathan Ross is anything to go by, we’re in danger of merely replacing one form of tasteless patronage with another.
Urged on by an audience which he appeared to have bought by the yard from Rent-A-Yob Mr Ross first extracted the urine from an unassuming, champion turkey-plucker, Mr Pilkington.
[…]
Mr Ross then announced with a flourish, the world premier of the latest adventures of the Gold Blend couple, asking: “After nine adverts, will he finally get to play hide the sausage?”
He didn’t and after the screening Mr Ross, ever master of that exquisitely sensitive instrument, the English language, insiively [sic] commented: “They never get round to shagging, do they?”

7-: From the column Odd Man Out, by Martyn Harris, published in The Daily Telegraph (London, England) of Saturday 17^th July 1993—Miss McLean is the headmistress:

The St Aidan’s concert this year is Joseph And The Amazing Technicolour Dreamcoat […].
[…]
OF COURSE the story has been cleaned up of the sex and violence, but as I’ve never been to a Lloyd Webber before, I don’t know if the bowdlerisation is Tim Rice’s or Miss McLean’s. There is not much about dipping the dreamcoat in kid’s blood, or about Potiphar’s wife “casting her evil eye” on Joseph and framing him on rape charges when he won’t play hide the sausage.

8-: From an extract from The Making of Priscilla, by the Australian film producer Al Clark, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Monday 12^th December 1994:

[Terence] Stamp is naturally anxious about his hair, make-up and wardrobe if he is to succeed in a role so hazardous that failure, he feels sure, will lead to ridicule. He is also concerned about his co-star. Not about the two other leading actors with whom he will spend the majority of his screen time, but about who will play Bob, the outback garage mechanic who develops an attachment to Bernadette and with whom he ends up, as the script so poetically calls it, “playing hide the sausage”.

9-: From It’s just not cricket.. Invasion of the Barmy Army, by Colin Wills, published in the Sunday Mirror (London, England) of Sunday 11^th June 1995:

Cricket, the last bastion of sporting understatement, is under siege from a new kind of fan. Loud, boisterous, beery, all-singing, all-dancing—and predominantly young.
They call themselves The Barmy Army and they bring the noise and passion of the streets to this cathedral of white flannel. […]
[…]
The Army cut its teeth on the Ashes tour of Australia last winter—and the Aussies loved them, give or take the odd drenching with beer.
[…]
Dave Peacock, the Army’s leader and known as The General, says: “[…] Yeah, and there were groupies, we got so famous in Australia. It wasn’t only the batsmen who scored. Essex Col did particularly well in that department.
HE’D come up to Mike Gatting the batsman and tell him about his sexual adventures.
“‘Ere Mike, I played hide the sausage again last night,’ he’d say and Mike would roar with laughter.”

10-: From the following, by Bianca Nogrady, one of the editors of Woroni, published in Woroni (Canberra, Australian Capital Territory, Australia) of Thursday 19^th October 1995—Woroni is the student newspaper of the Australian National University:

A major highlight of the Woroni year would have to be watching Andrew and Janina trying desperately to fit the word ‘skullfuck’ into every edition somewhere; a kind of literary ‘Hide-the-Sausage’.

11-: From Tharunka (Kensington, New South Wales, Australia) of Tuesday 23^rd April 1996—Tharunka is the student newspaper of the University of New South Wales:

– – – sweetie???
– – – darling!!!

Unleashed into the venereal world of University Sexuality the Sirens of the Salacious are ready to establish their own School—the Faculty of F**k.
Darling: I just don’t see the bloody point, Sweetie.
Sweetie: Of Sexuality Week, Darls?
[…]
Darling: The whole point of the damned Sex Week is to educate the masses on how insert tab A into slot bloody B. Or whatever.
Sweetie: Whatever?
Darling: Well not everyone is into playing only hide the sausage!

12-: From Queer Core: Lessons to live by, by Nathan Hart, published in Tharunka (Kensington, New South Wales, Australia) of Tuesday 29^th October 1996:

9) Research has shown it takes 7 schooners before your average engineering student will consent to letting you play hide the sausage with his behind. Warning—if he doesn’t let you stop you are in trouble.

13-: From Odd sex-amples of human behaviour, by John Harper, published in the Tamworth Herald (Tamworth, Staffordshire, England) of Friday 21^st November 1997:

What they call ‘it’

After ‘making love’ and ‘bonking’, the top intimate terms for ‘it’ are:
● Nookie
● Rumpy Pumpy
● Hanky Panky
● A Bit of the Other
● Early Night
● Wham-Bam
● Hide the sausage
● Dunking doughnuts
Some of the weirdest names are: Cuddly Wuddlies; Tiddlywinks; Bucking the Bronco; Toad in the Hole; Bolting the Banana; Potting the Pink; Introducing the Ferret; Park the Car; Playing Trains and Tunnels; Mr Wobbly Hides his Helmet.