I found more sources that address the possible repercussions of WWI for British philosophy (and esp. for British analytic philosophy).
First, Deakin University hosted a conference in November, 2014, called 'Crisis and reconfigurations: 100 years of European Thought Since 1914'. I think that a collection of papers from this conference is going to be published. It looks like the papers are mostly about continental philosophy, but one item, by Andreas Vrahimis (pdf), examines analytic philosophy.
Also, historian Peter Hoeres has an article called 'Idealism as Transnational War Philosophy, 1914-1918'. It appears in Anglo-German Scholarly Networks in the Long Nineteenth Century (ed. Heather Ellis and Ulrike Kirchberger).
Here's a rough sketch of some hypotheses about the War's influence on British philosophy.
1. The War discredited whatever philosophies formed the status quo in universities before 1914. Thus, in Germany, the War finished off neo-Kantianism; in the UK, it dispatched absolute idealism. This conjecture is neutral vis-à-vis the content of the status quo philosophy. It is vulnerable to a similar objection to the one that I leveled at Candlish's proposal; viz., there's little evidence that any of the British philosophers who had first-hand experience of the slaughter were led to change their philosophical views, and, more generally, it's hard to find any established philosopher in the UK whose philosophy underwent a major change due to the War (with the possible exception of Sir James Black Baillie). To avoid this difficulty, a proponent of this first hypothesis must recast it as a claim about the War's influence on only those individuals who became philosophers after the War (and not on those people who already were established philosophy academics when the War began). (Indeed, let's attach this caveat to all three of the hypotheses that I canvas in this note.)
Even then, this content-neutral hypothesis is much more plausible about the War's influence in countries that lost the War. For instance, it looks like the total, unambiguous collapse of the Wilhelmine Reich did unleash much creative energy (in addition to destructive forces) in diverse, Weimar arts and sciences; such a widespread discrediting of the old order is bound to be followed by radical questioning of old assumptions and by the ascendancy of 'new ways of thinking'. But the UK perhaps did not experience any sudden discrediting of the old order. Perhaps it was only later, after the publication of war memoirs (mainly in the 1920s) and after the War's economic costs had grown more apparent, that old attitudes began to be questioned.
2. Prior to the War, philosophers had been adrift in airy speculation, and the War brought them back to earth, to more humble inquiries that at least held the promise of uncovering some truths. Switching metaphors, it was out with the grandiose, a priori houses of cards, and in with careful, humble attending to facts (more Cook Wilson, less Bradley).
Theology saw a similar post-war development. Neo-orthodox theologians (e.g., Barth and Brunner) chastised the pre-War, German theologians (many of whom supported going to war) for having been lost in abstruse, academic disputes. (Such complaints echoed the Protestant propaganda about medieval schoolmen trying to determine the number of angels that can dance on a needle's point. This Protestant trope was taken up in Milton's Paradise Lost [in the figure of the demons 'in wandering mazes lost'].)
Use of this sort of trope should be expected after a calamity. People reflect on the calamity and decide that it owed (partly) to some decadent trend that was evident before things took such a dire turn (e.g., Spengler). The complaint may be directed at benighted academics, who stand accused of leading people astray in fruitless speculations on irrelevant matters. The corrective requires getting back to a neglected locus of truth that had all along been accessible. In its religious version, this locus is a source of revelation (such as the Bible); but in its secular version, some other previously ignored but accessible source of enlightenment must be posited. This source might be experience, so that one could expect to hear calls for a return to the empirical focus of earlier British philosophy. Also, there might be a call to get back to the rigorous examination of facts, and the accessible facts in question might involve words and the logic of their use.
So, perhaps one impact of the War was to drive British philosophers towards empiricism and a greater focus on the minutiae of language, trends that certainly were prominent (in varying degrees) among positivists and ordinary-language philosophers.
3. Before the War, idealists offered philosophical theories of politics and society. After the War, philosophers were reluctant to try to make sense of such human affairs. 'Look how absurd it all is,' they seemed to say, 'all these millions killed for no good reason. There's no sense in any of it.' So, don't bother trying to find sense where there isn't any; don't waste time on some philosophy of social or political matters.
The inter-war years did see a retreat of British philosophy from explicit engagement with politics. Could this have been due, in part, to a sense of the absurdity of human affairs? Was it partly due to the example of Russell, whose political activities in the War got him booted from academia, or of Otto Neurath, who was also imprisoned for his political activities? Was it partly due to the vilification of idealist political philosophy by L. T. Hobhouse and others (on the grounds that it had been inspired by German philosophy)? Seeing Bosanquet's philosophy condemned in this way and seeing Russell's sacrifice may well have dissuaded British philosophers from having much to say about politics. The sentiment may have been, 'You'll only get your fingers burned if you write about politics (in a practical or even theoretical way).'
In his above-cited paper, Andreas Vrahimis analyzes the growing silence of analytic philosophers on matters political. Vrahimis cites a discussion of this topic by Jack Reynolds. I can't find a copy of Reynolds' paper, but judging from its Abstract, Reynolds (like Vrahimis) takes the War to have exacerbated the then-recent divide between analytic and continental philosophy. One factor in this growing divide, according to Reynolds (according to Vrahimis), is continental philosophy's connection to political questions and the relative lack of such a connection in analytic philosophy. Vrahimis draws attention to Neurath's radical political program and to Neurath's claim that his program would be helped by the removal of metaphysics from politics. (Vrahimis, 'Legacies of German Idealism' Parrhesia 24 : 99) For Vrahimis, Neurath's example shows that analytic philosophy's retreat from theorizing about politics was itself a self-consciously political move. However, in the UK, it was analytic philosophers more generally, and not just positivists, who seldom ventured into political theory after the War. (Interestingly, two of the analytic philosophers who wrote the most about politics in the mid-20th Century were WWI veterans: Mabbott and Weldon.)
One hypothesis I haven't addressed is a more specific application to philosophy of the general idea that the War undermined Whiggish views of history. Assumptions about intellectual or moral progress were re-examined and often rejected. This idea is explored by Mark Bevir and Naomi Choi in 'Anglophone Historicisms'. (Journal of the Philosophy of History 9 : 327-46, esp. at 332) Here's Rupert Read on a similar theme.