Who are the "Millennial Folk" being referred to here?

The book by Michael Nicholson from 1992 quoted in the question is slightly incorrect and thus essentially misquotes Taylor.

Taylor references and quotes Repington as "millenian folk". (src, p2):

1. In contemporary parlance, the war of 1914–18 was always, not surprisingly, the Great War. It did not need the war of 1939–45 to change it into the first World war. Repington devised the phrase at the time of the armistice, 'to prevent the millenian folk from forgetting that the history of the world is the history of war*. Repington, The First World War, ii. 291.

— A. J. P. Taylor: "English History 1914–1945", Oxford University Press: Oxford, New York, 1965, p26.

Unfortunately, this quote and reference mangling continues even further back:

The phrase used by Mr Repington actually reads: "millennium folk" (although Taylor gives the page number as 291, my edition of Repington has it at 391. archive.org)

I saw Major Johnstone, the Harvard Professor who is here to lay the bases of an American History. We discussed the right name of the war. I said that we called it now The War, but that this could not last. The Napoleonic War was The Great War. To call it The German War was too much flattery for the Boche. I suggested The World War as a shade better title, and finally we mutually agreed to call it The First World War in order to prevent the millennium folk from forgetting that the history of the world was the history of war.

— Charles à Court Repington: "The First World War 1914-1918", Volume II, Constable and Company: London, 1920, p391.

This in turn is clearly meant to play on

Millenarianism (also millenarism), from Latin mīllēnārius "containing a thousand", is the belief by a religious, social, or political group or movement in a coming fundamental transformation of society, after which "all things will be changed". Millenarianism exists in various cultures and religions worldwide, with various interpretations of what constitutes a transformation. […]

While many millennial groups are pacifistic, […]

The OED editor concurs:

This is the earliest known occurrence of First World War. When we hear or use the phrase now, we think of the First World War, in contradistinction to the Second, and intuitively we expect the phrase was coined in or after 1939. In fact, first was used in anticipation, not retrospect: Repington was very consciously distinguishing the 1914-18 war from former wars, and aligning it with possible future ones. The phrase acknowledged not only the unprecedented scale of the conflict (the First World War), but also predicted its enduring historical significance. It suggested that – far from being the war to end all wars – this might be the first of a new kind of global conflict. The name was conceived as a warning from history.

Note that this "warning from history" did not have the effect of ushering in one thousand years of peace, obviously, now, but it did have an effect on Taylor, who wrote "is the history of war"; thus hyper-correcting Repington's quote who wrote actually "was the history of war".

In other words, Repington means just people hoping that this would have been indeed 'the war to end all wars', or simply 'pacifists', here in a mainly religiously-Chritianity motivated variant:

[…] advocated for nonresistance against the institution of slavery and imperialism, as they saw the Bible as the embodiment of “passive nonresistance” and the only way to achieve the new millennium on Earth.

Or alternatively:

Postmillennalism reemerged in the late-19th century. The Social Gospel movement, popular among liberal Protestant clergy, labor organizers, and urban reformers, contained a strong focus on the coming millennial “Kingdom of God” that combined millennial visions with a focus on modern industrial and social problems. Walter Rauschenbusch (1861–1918), the most popular Social Gospel theologian in America before World War I, argued that by heeding Jesus’ teachings humans could realize the Millennium – the Kingdom of God – on earth. Though it is easy to overemphasize the shock of World War I to the vitality of the Social Gospel, postmillennialist anticipation of the kingdom’s realization ebbed as European and North American societies descended into two world wars.

— "Millennium, Millennialism", Encyclopedia of the Bible and Its Reception Online, edited by Christina Hoegen-Rohls, Daniel Hummel, Younghwa Kim, Richard Landes, Jan Rohls, Theresa Sanders and Michael Sommer, deGruyter, 2021.

As seen in

— Alexander Tyrrell: "Making the Millennium: The Mid-Nineteenth Century Peace Movement", The Historical Journal, Vol. 21, No. 1 1978, pp. 75–95 jstor

The Oxford English Dictionary therefore gives the definition:

3. fig. and in figurative context: A period of happiness and benign government

millennium Hence millenniumism, the doctrine of the millennium. millenniumite, one who believes in the millennium.

— From Oxford English Dictionary, 2nd Edition

Thus, the usage often in collocations as 'millennium of peace', spread even beyond Christianity-motivated circles, like in

[…] the millennium may yet be brought about through the honest trading instincts of man (gBooks: — The Peace Movement: The Organ of the International Peace Movement, 1913),

Or even for military audiences who expected that the aeroplane would make battle ships so obsolete as to usher in a "millennium of peace" (— Victor Lougheed: "The Aeroplane vs the Battleship", Popular Mechanics, Dec, 1910. gBooks)

BTW, the QI episode originating this is of the better David Mitchel episodes (YouTube, "QI - Series 9 Ep 2", 1 minute 20 short clip, full version, webpage for that episode, quoting Repington correctly.)