The self-explanatory phrase as useful, or as much use, as an ashtray on a motorbike means utterly useless.
These are the earliest occurrences that I have found, in chronological order:
1-: From the Sunday Mirror (London, England) of Sunday 19th April 1981:
Readers pass on apt descriptions they have for people . . .
My dad says I’m as much use as a one-legged man in a backside-kicking contest.—William Dudfield, aged 11, Badsey, Worcs.
A pal of mine says of his workmate: “He’s as useful to me as one chopstick is to a Chinaman.”—James House, Bracknell, Berks.
I’m as much use as an ashtray on a motorbike, according to my husband.—Mrs. Frances Keightley, Middlesbrough, Cleveland.
2-: From Frank advice, published in the Harrow Midweek (London, England) of Tuesday 18th January 1983:
“Darling, I’m EVER so sorry, REALLY . . . you’ve obviously gone to endless trouble . . . but I have told you about Frank, haven’t I?” On cue, a mental picture appears, floating just in front of your brain somewhere of a sallow faced, unsmiling bloke with spectacles and about as useful as an ashtray on a motorbike when it comes to enlivening a gathering.
Pam’s husband. Yes, you remember Frank all right.
Wendy’s talking again: “He’s ever so fussy about his food—hates anything spiced, or fancy as he calls it. I don’t suppose, darling—you could manage to do him steak, chips and peas separately?”
3-: From an article about the funding of the Students’ Association, by Oliver Raymond, 2nd year Geology student, published in Woroni (Canberra, Australian Capital Territory, Australia) of Wednesday 12th October 1983 (Woroni, the title of the student newspaper of the Australian National University (ANU), based in Canberra, is an Indigenous-Australian word meaning mouthpiece):
Few students read this publication [= the Counter Course Handbook] and even fewer take any notice of it, despite the Lefties claim of its great benefit. (Any science student knows it is about as useful as an ashtray on a motorbike.)
4-: From How bureaucrats are killing off the blacksmiths, by David Tremellen, welding engineer, published in The Guardian (London and Manchester, England) of Saturday 14th January 1984:
Where a craftsman and an apprentice are working on a one-to-one basis the HSE [= Health and Safety Executive] is about as useful as an ashtray on a motorbike.
5-: From Radio choice, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Thursday 9th February 1984:
11 pm, 2MBS-FM, Like a bridge under troubled waters or an ashtray on a motorbike, some things come easily to lateral thinkers. Might Get Lost, which features in tonight’s edition of Contemporary Editions, is a radio play by Les Gilbert which is hardly what you’d call “typically Shakespearean”. Much of it is recorded under water and uses strange techniques to explore the notion that people use sound to determine where and who they are. Let us hope we’ll learn how the Hollywood Symphony Orchestra manages to play so beautifully beneath the waves in films such as Jaws, The Poseidon Adventure and Thunderball.
6-: From Air Florida getting $6 million for pay, published in the Daily World (Opelousas, Louisiana, USA) of Friday 6th July 1984:
Miami (AP)—Air Florida, grounded when it filed for bankruptcy protection, has been granted use of $6 million to pay the salaries of laid-off employees. […]
Passengers were stranded when other airlines refused to honor Air Florida tickets except on a standby basis.
The Portobello Thistle Boys Soccer Club of Edinburgh, Scotland, which had bought 43 round-trip tickets to Tampa, was among those affected. The boys, family members and club leaders are being housed by families in Land O’Lake, Fla., while they solve their problem of how to return to Britain.
“We’ve got 43 Air Florida tickets, and they’re about as useful as an ashtray on a motorbike or a concrete parachute,” said John Kelly, 29, the leader of the club.