Especially in phrases such as as much use as a chocolate teapot, the British- and Irish-English expression chocolate teapot, and its variants, are used of something or someone that is utterly ineffectual.
—Synonym: as useful as an ashtray on a motorbike.

The earliest occurrences of the expression chocolate teapot that I have found are as follows, in chronological order:

1-: From Coffee Cup Reading, published in the Democrat and Chronicle (Rochester, New York, USA) of Wednesday 14^th June 1967:

Shades of Bunker Hill! *
By Don Berry

Blimey! It was a helluva shock at first.
There I was with a couple of other Englishmen at Aquinas Stadium last night to watch London’s Chelsea soccer team show Americans that the only real type of football is one you play with your feet.
We sat talking loudly in obvious British accents to impress on our neighbors that they were next to a trio of experts from the country where the game was born. With courteous superiority we answered our neighbors’ queries on subtle points like the markings on the field (which weren’t too clear, incidentally).
All in all we were ready to smile knowingly as British superiority on the American continent grew again.
Then it happened. The game had hardly started. If it had been televised, there wouldn’t even have been time for a commercial break when—crunch—Chelsea’s defense was in a shambles and the Rochester Lancers were a goal ahead.
For a moment it looked like Bunker Hill all over again.
But even soccer players have stiff upper lips in England. And by the time the game reached half-time, Chelsea had given us back our self respect with five goals. They added a sixth after halftime.
The crowd tried its best to rally the home team. And its partisanship was quite a feat when you consider that many of the “home” boys came from places like Italy, Brazil and the Argentine. The British threat obviously united them all. But it didn’t help.
The crowd’s reactions showed the finer points of the game and its rules—including the fiendishly complicated offside rule—are not a mystery here.
In fact, the main thing which distinguished the crowd from a typical British soccer crowd was its politeness to players and referee.
I missed not hearing somebody scream at a player: “You’re no more use than a chocolate teapot!” Or someone else questioning the eyesight, mental stability and parenthood of the referee in one nicely turned, if unprintable, phrase.
But if the game catches on—and an attendance of more than 6,000 is a good omen—no doubt the crowd will develop some style in its shouting as well.

* This refers to the Battle of Bunker Hill, in Charlestown, Massachusetts, on Saturday 17^th June 1775, during the War of American Independence (1775-83).

2-: From Nomads go nap against Ramblers’ nine men, about Chester Nomads AFC (Association Football Club), by ‘Nomad’, published in the Cheshire Observer (Chester, Cheshire, England) of Friday 3^rd November 1972:

The third XI these days are about as much use as a chocolate teapot. The fixture secretary should seriously consider revising their opponents, and perhaps, match the ailing players against Junior schools in the Chester area. And it had better be the second teams. On Saturday they travelled to Bangor Normal College, where they had a lovely view of the Menai Strait—and Colin Stockton picking the ball out of the net seven times.

3-: From Sex Manual Sans Plain Brown Wrapper, by Jean Sharley Taylor, an interview of the British scientist and physician Alexander Comfort (1920-2000), who had just published The Joy of Sex: A Gourmet Guide to Love Making (New York: Crown Publishers, Inc., 1972)—interview published in the Los Angeles Times (Los Angeles, California, USA) of Sunday 5^th November 1972:

“I organized the book because of the extremely poor standard of counseling going on. I found when I wrote biological articles about sexual behavior, scads of letters came from all over Britain; people with quite simple sexual problems, really.
“I’d write, advising them to see their doctors and the answers came back, ‘I did see him and he’s a nut.’ Seeing one’s doctor, I concluded, is about as much good as using a chocolate teapot.”

4-: From Red Shift (London: William Collins Sons & Company Ltd, 1973), by the English novelist Alan Garner (born 1934):

“You great wet Nelly,” said his father. “You’re as much use as a chocolate teapot.”

5-: From Stars on Saturday, by Colin Wills, published in the Sunday Mirror (London, England) of Sunday 21^st August 1977:

Look who’s behind you at the soccer match

Here we go again. Another football season. And it will have its moments of joy and depression for the stars as well as the rest of us as they follow their favourite clubs.
So when you get tired of watching players slobbering over each other and fans clobbering each other, why not cast your eye around? You never know who might be standing next to you…
[…]
TV chat-show host Michael Parkinson bemoans the fact that the natural wit of the terraces has been replaced by mindless chants and filthy songs.
He harks back to his boyhood watching Barnsley, and the day the club played a new and expensive full back; alas, the new man made a hash of everything he did.
His performance infuriated the fan standing next to Mike, and Mike could see him racking his brain for the perfect damning phrase for the costly flop.
At last he hit on it: “Thou art about as much use,” he shouted, in his rich Yorkshire accent, “as a chocolate teapot!”

6-: From Barnsley bashers face the chop, by Michael Parkin, published in The Guardian (London and Manchester, England) of Monday 17^th July 1978:

Barnsley, the most grievously mocked town in Yorkshire, is preparing to open a tourist information centre in a converted shop.
Tourists contemplating a visit should ignore press references to Barnsley, where local “lads” were said to have angered a cafe owner by drinking his sauce bottles dry, and where a ballroom dancer read a report of Barnsley Town’s latest match in a football newspaper held behind his partner’s back.
You will no longer find the hotel night porter who, when asked by a guest to carry his suitcase upstairs, looked him up and down and replied, “Tha looks fit enough. Carry it thisen.”
Barnsley is emerging from its lack of sophistication, but much of its agreeable character lingers on. You can still go into a Barnsley pub and hear a miner say of a friend who has excused himself from buying a round: “It’s only him and t’ Queen as doesn’t carry any money.”
Tourists that go to home games of Barnsley Town will hear some of the finest football wit and repartee in the land. Players are accused of being “as nimble as a stone trough” or “as much use as a chocolate teapot.”

7-: From Mission impossible: Peter Taylor reports from the Middle East on the troubled UN ‘peacekeepers’, published in the Sunday Telegraph (London, England) of Sunday 1^st July 1979—UNIFIL is the abbreviation of United Nations Interim Force in Lebanon:

Unifil is, by common consent, of as much use as a chocolate teapot.

8-: From the review of Rust Never Sleeps, an album by Neil Young and Crazy Horse, published in the East Kent Times and Mail (Ramsgate, Kent, England) of Friday 6^th July 1979:

‘RUST NEVER SLEEPS’ proves to be rather a negative musical statement—rust might not sleep but Young’s awareness of the ever-changing fickle world of rock music appears dormant.
However, there are one or two tasty morsels here—witness his superb execution of ‘Powderfinger’ and ‘Sedan Delivery’.
The band are also firing on all cylinders on ‘Hey, Hey, My, My (Into the Black)’ but that’s just about it. The rest of the songs are as useful as a chocolate teapot.

These are three occurrences of the variants chocolate kettle, chocolate fireplace and chocolate fireguard:

1-: From the column Sounds, by Phil Penfold, about the Eurovision Song Contest, published in the Evening Chronicle (Newcastle upon Tyne, Tyne and Wear, England) of Saturday 10^th March 1979:

We always get lumbered with inane, chant-along rubbish by a group or singer who has about as much belief in his or her product as I have in the usefulness of a chocolate fireguard.

2-: From a letter published in the Evening Herald (Dublin, County Dublin, Ireland) of Thursday 23^rd June 1994:

I wish to complain about the people employed in positions of authority with Dublin Bus, and with larnroid Eireann.
[…]
The people in larnroid Eireann who have spent millions of pounds of Irish money on a fleet of new Japanese railcars, which so far have a reliability record like a chocolate kettle.

3-: From an interview of the British singer-songwriter and motorcycle racer James Toseland (born 1980), by Andrew Baker, published in The Daily Telegraph (London, England) of Friday 18^th February 2005:

On top of all his promotional commitments, Toseland is in the process of moving to the Isle of Man (“a complete nightmare”) and has just completed two days’ testing for his Xerox Ducati team in Spain. “It rained the whole time we were there. So we got a good wet set-up on the bike, but since the first race is in Qatar, that’s about as much use as a chocolate fireplace.”