The British-English phrase to be unable to run a whelk stall and its variants mean to be incapable of managing the simplest task or enterprise.
—Synonyms:
– couldn’t organise a piss-up in a brewery;
– couldn’t lead a flock of homing pigeons.

The phrase to be unable to run a whelk stall was coined by John Elliot Burns (1858-1943), English trade unionist and politician, in the New Year’s address that he gave on Sunday 7^th January 1894 to his constituents of Battersea, County of London; the following is from the transcript of this address published in Reynolds’s Newspaper (London) of Sunday 14^th January 1894:

“I am told,” he went on, “that we (himself and some other Labour members) are to be opposed. Let opposition come. I am to be opposed by a banker on one side and by bigots on the other. I shall wipe the floor with both of them. (Mighty cheering.) Finance and fanaticism are to fight against a Labour man like myself. I have come here to show my friends and enemies in this district my intentions. If I am fought here, I will carry the fight to every constituency where the men who fight me are standing. From whom am I to take my marching orders? From adventurers and ne’er-do-weols [sic] who are in the Labour movement for what they can make out of it? Am I to take my orders from these political Admirable Crichtons who fancy themselves Pitts¹ and Bolingbrokes², but who haven’t got the brains and the ability to run a whelk stall!”—at which there was another outburst of cheers and laughter.

¹ William Pitt (1708-78), 1^st Earl of Chatham, British statesman
² Henry St John (1678-1751), 1^st Viscount Bolingbroke, English politician, government official and political philosopher

A certain Walter Isaac alluded to the image used by John Burns in a letter published in the Islington Daily Gazette and North London Tribune (London) on Friday 2^nd January 1903:

I cannot believe that the public generally are aware of the recent extraordinary proceedings of the Baths Committee. Their management of these great establishments, serving so many useful purposes, has never been characterised by even a moderate display of business ability, and reminds us somewhat of Mr. John Burns’ description of some public committee as not possessing sufficient ability to run a whelk stall.

The earliest instance that I have found of the phrase without reference to John Burns is from the following paragraph published in The Lancashire Daily Post (Preston, Lancashire) of Tuesday 21^st February 1905 (the he after the word opponents is erroneous):

LABOUR CANDIDATE’S PLAIN LANGUAGE.

Mr. T. F. Richards, Labour candidate for Wolverhampton West, told a meeting of electors that politics were very low down there. Votes were purchased with beer. He should not show himself on platforms, at football matches, in cricket fields, nor on cycle tracks. For his opponents he would say that he was a miserable working man. He went to work before he was 13. He was a trades union official, and a paid agitator. (Laughter.) The Government, he said, had not enough intelligence to run a whelk stall. (Laughter.)

The phrase seems to have been popular among Labour Party members; on Wednesday 19^th May 1926, several newspapers—for example The Scotsman (Edinburgh, Scotland)—reported that the previous day James Ramsay MacDonald (1866-1937), leader of the Labour Party, had declared, about the government of Stanley Baldwin (1867-1947), leader of the Conservative Party:

“When I see my colleagues and myself pilloried as makers of strife,” Mr MacDonald declared, “it goes like a barbed arrow right into my soul when I remember how we have striven for peace. I am sometimes driven almost to despair regarding the future of my country. The intention is good, the masses are glorious, but your Government could not run a whelk stall.”

The following day, the Conservative politician William Joynson-Hicks (1865-1932), then Home Secretary, returned this remark against its author—the following is from The Evening News and Southern Daily Mail (Portsmouth, Hampshire) of Thursday 20^th May 1926:

The jibe of Mr. Ramsay MacDonald that the Government was not fit to run a whelk stall was referred to to-day by Sir William Joynson Hicks, at a special meeting of the Grand Council of the Primrose League in London.
“He may be right” Sir William declared, “but we have rather successfully run the country during the last few days. I will not be so rude to Mr. MacDonald as to suggest he is not fit to not run a whelk stall. I think he may be quite capable of doing it. But difficulty arose when a body of men, whose capacity was that of running a whelk stall, strived to run the country.”

The following paragraph is from the humoristic column Bon Mot-Ifs, by Hartley Carrick, in The Bystander (London) of Wednesday 16^th June 1926:

We understand that some supporters of the Government who disagree with Mr. MacDonald’s contention that it couldn’t run a whelk stall, have formed themselves into a Whelkome Club.