Composed of a blend of the surnames Butler and Gaitskell and of the suffix -ism, the noun Butskellism originally denoted the economic policy of Richard Austen ‘Rab’ Butler (1902-1982), Conservative Chancellor of the Exchequer from 1951 to 1955, regarded as largely indistinguishable from that of Hugh Todd Naylor Gaitskell (1906-1963), Labour Chancellor of the Exchequer from 1950 to 1951 and subsequently Shadow Chancellor.

The noun Butskellism occurs, for example, in Brexit, the environment, energy bills … it’s hard to tell Labour and Tory policies apart, by Larry Elliott, economic editor, published in The Guardian (London and Manchester, England) of 1^st June 2023:

Back in the 1950s, a term was coined to describe the consensus that had allegedly emerged over the way to run the economy in the postwar world. An amalgam of the names of two chancellors of the exchequer—Rab Butler for the Tories and Hugh Gaitskell for Labour—it became known as Butskellism.
[…]
Whisper it softly, but Butskellism has returned. While there are still areas where the Conservatives and Labour disagree, these tend to be managerial and technical rather than ideological. On the big issues not much separates them, with both parties shifting towards the centre in recent years. For want of a better word, let’s call it Reevuntism in honour of the shadow chancellor, Rachel Reeves, and the man she wants to replace at the Treasury, Jeremy Hunt (the Economist has gone for Mr Heeves).

The noun Butskellism is first recorded in Mr Butskell’s Dilemma, by the British journalist Norman Macrae (1923-2010), published in The Economist (London, England) of 13^th February 1954:

The next few weeks will show whether the Opposition will seize this chance of golden silence; or whether, in a Brown fury, it is going to throw the opportunity for constructive Butskellism away.

In his article, Norman Macrae also used Butskell as the proper name of a fictitious composite of Butler and Gaitskell:

Mr Butskell is already a well-known figure in dinner table conversations in both Westminster and Whitehall, and the time has come to introduce him to a wider audience. He is a composite of the present Chancellor and the previous one (any resemblance to certain other historical characters, such as Sir Robert Peel—or Sir Robert Boothby—is purely imaginary). Whenever there is a tendency to excess Conservatism within the Conservative party—such as a clamour for too much imperial preference, for a wild dash to convertibility, or even for a little more unemployment to teach the workers a lesson—Mr Butskell speaks up for the cause of moderation from the Government side of the House; when there is a clamour for even graver irresponsibilities from the Labour benches, Mr Butskell has hitherto spoken up from the other.

According to the Oxford English Dictionary (online edition, December 2021), the British journalist Ian Trethowan (1922-1990) attributed the coinage of Butskellism to the British Conservative politician Richard Fort (1907-1959) in a private letter to the British civil servant and businessman Edward Playfair (1909-1999) in 1987:

Yes, he [i.e., Richard Fort] did invent ‘Butskellism’. It was over lunch at the Reform; Norman McRae (our host) completed the trio […] We were having a general discussion about the political-cum-economic situation, and it is our recollection that Richard coined the actual word. Norman then went off and wrote the Economist leader.

The noun Butskellism later came to denote, more generally, the centrist attitudes and policies of both Labour and Conservative parties during the post-war period, which led to an unexpected measure of agreement on such matters as law, education, social policy and defence.

This is illustrated by the second-earliest occurrence of Butskellism that I have found, from a letter to the Editor, by one David Hatton, published in the Evening Sentinel (Stoke-on-Trent, Staffordshire, England) of 24^th December 1954:

To the ordinary person, there may seem little difference between the tactics of Right-wing Socialists and Left-wing Conservatives—the policy of “Butskellism,” as it has been aptly called.

Derived from the noun Butskellism, the noun Butskellite designates a supporter of Butskellism. The earliest occurrence of Butskellite that I have found is from an account of the International Conference on the Future of Freedom, convened by the Congress for Cultural Freedom and held in Milan (Italy) from 12^th  to 17^th September 1955—account titled L’Avvenire della Libertà, by the British historian Max Beloff (1913-1999), published in The Spectator (London, England) of 30^th September 1955:

We discussed freedom’s internal, as well as its external, enemies; and for some the ‘Butskellites,’ strongly represented in the British and American, and to some extent in the French, delegations, were the real enemy. For some the real devil was precisely the Welfare State—gently denounced by Professor F. A. Hayek, and more stridently by the Cobdenites * of West Germany and Italy, for whom any State intervention in economic life could only be a prelude to the ultimate totalitarian tyranny.

(* The noun Cobdenite designates a supporter of Cobdenism, a policy advocating free trade, peace and international cooperation. The reference is to Richard Cobden (1804-1865), a British politician and a campaigner for free trade and peace.)

Derived from the noun Butskellism, the adjective Butskellist means characteristic of Butskellism. The earliest occurrence of Butskellist that I have found is from the following theatrical review, by the British critic Kenneth Tynan (1927-1980), published in The Observer (London, England) of 8^th January 1956:

JEAN-PAUL SARTRE’S Nekrassov (Unity), which I take to be the best political comedy we have seen since Shaw’s perihelion, could never have been written in a Butskellist society. It could have sprung only from a country where extremism is not yet a term of abuse, class-consciousness is still alive and kicking, and the worker’s loathing of the bourgeois is genial but ineradicable; in short, from France.