British Prime Ministers are either vicars or bookies: quote origin?

Question

The old adage has it that British prime ministers are either vicars or bookmakers. In Phoney Tony the country has a bookie masquerading as a vicar, a posture that does little for the standing of either profession.

-- Glen Newey, LRB, 2003

There are a few other mentions on the web of the form "Prime Ministers are either bookies or vicars", but not much that gives detail on earlier usage or how old it might be. I'd guess it is an older quote or saying that predates the web. Can anyone share an origin, or failing that, earlier examples?

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EDIT with more detail on research: Initial searches for the phrase on the web show very little. With the tip from @peterG that the variant "bookies or bishops" was more common, this led to an Anthony Crosland biography mentioning Hugh Gaitskell, and then to a thesis by Shack (PDF) p277 citing Muggeridge's book. This seemed solid enough to result in my answer below.

@JEL has since found Curran in 1956, predating it, in his answer.

Peter Hitchens suggests Alan Watkins in his Daily Mail column in 2017. This is technically possible as he would have been 23 in 1956, but not the greatest source without further support.

Answer 1

Apparently, the phrase is from an article in The Spectator (paywalled), 6 April 1956, p. 8, by Charles Curran. In an article titled "Liberty, Equality, and Mr. Gaitskell", the subsection titled "The Professors Take Over" starts with

To become a successful political leader in Great Britain you must be either a bishop or a bookmaker. The bishops are a distinguished lot — from Gladstone, the greatest of them all, to Balfour, Asquith, Cripps, Attlee, Eden, Butler. So are bookmakers — Disraeli, Lloyd George, Churchill, Mr. Bevan.

The tragedy of British Socialism is that its leadership has now fallen into the hands of men who are neither bishops nor bookmakers but professors; men with neither fervour nor gusto, who shrink both from the cakes and from the ale.

The lead-in to this from the main article ("Liberty, Equality, and Mr. Gaitskell") is

Skilfully coated, a bolus of self-contradictory absurdities can be fed with ease to a large part of the mass electorate. The entire history of British Socialism, from the 1890s to 1945, demonstrates this truth. Egalitarianism is no more discreditable, in propaganda terms, than was 'Stand up to Hitler and abolish the Army' or its post-war equivalents 'Cut the taxes and restore the subsidies.'

But how many votes are there likely to be in egalitarianism? To answer that question, let us look first at the people who are playing with it.

Curran's bon mot is then paraphrased in an essay by David Marquand, "Sir Stafford Cripps: The dollar crisis and devaluation", included in a 1963 volume titled The Age of Austerity (last paragraph, p. 159):

As Mr. Charles Curran once remarked, the British people like their leaders to resemble either bishops or bookies.

Answer 2

To comfort him I developed on the spur of the moment a theory, often propounded subsequently - that to succeed pre-eminently in English public life it is necessary to conform either to the popular image of a bookie or of a clergyman; Churchill being a perfect example of the former, Halifax of the latter. -- p45, Malcolm Muggeridge, The Infernal Grove, 1973

There might still be an earlier one, or he may be repeating himself from earlier journalism, or both.

The tip from @peterG in the comments led me down the right rabbit hole. The "bishops" version does seem much more popular than "vicars".