Perhaps the best known British writer on 'Time' during the 20th century was not J.W. Dunne himself, but his interpreter and populariser J.B. Priestley (1894-1984).
Priestley is hardly known nowadays except perhaps for his play An Inspector Calls (although, to be remembered for even a single play which stays in the commercial repertory is more than most playwrights achieve - it is as much as, say Oliver Goldsmith or Oscar Wilde achieved).
However, in his heyday, from the 1930s to the 1960s, Priestley was one of the best known 'public intellectuals' of the UK. He had written big-selling and critically-respected novels, travel, books, plays, essays; and was a very popular radio and television broadcaster: was was indeed awarded the Order of Merit (OM) which is the highest intellectual accolade in the British honours system.
Anyone who was interested by my earlier blog posts on J.W. Dunne should probably get hold of Priestley's Man and Time, 1964.
Overall, I find Priestley interesting rather than convincing. His mature views were transitional between a youthful atheism and socialism, and later partial reactionary and spiritual interests.
Likewise, his reflections on the nature of Time are stimulating but seem rather confused and therefore not compelling.
What he seems to have done, in general, was outline problems worthy of attention.
In terms of Time, Priestley took seriously his own experiences of a different kind of Time (or several different kinds of Times) than the usual linear, serial treadmill leading inexorably to death and extinction.
These other Times seemed to supervene in situations like aesthetic absorption, the act of creation, and of course dreams.
Priestley was convinced from his own experience and some hundreds of accounts of others which he gathered (as well as from the work of Dunne's) that dreams could be pre-cognitive.
He also became convinced in the survival of the soul after death, probably in another kind of time.
Working wholly within a secular framework, he didn't explain these conclusions satisfactorily; indeed his explanations seem pretty poor to me - presumably because his assmptions rule out any possible coherent answer.
Altogether, Priestley seems on the one hand an unjustly neglected figure, on the other hand not a major thinker - but worth a look.