Olaf Stapledon was older than Toynbee, but overlapped with him at Balliol (post on Balliol), where he read Modern History. A letter from Toynbee to Robert Darbishire of March 9 1913, published in the same volume as his correspondence with Columba Cary-Elwes, suggests that Toynbee was at least acquainted with him.
What follows comes from page images at Google Books, but I haven’t been able to read the rest to find out, from WHG Armytage, how close Stapledon’s examinations of future civilisations come to Toynbee’s of past and present ones. Stapledon seems to refer at one stage to an “Americanised world-state”, which fails “to discover fresh supplies of energy, which even in the Antarctic are becoming exhausted”. Armytage, who is described in various online pages as a eugenicist and published books on the history of education in England, refers to Last and First Men and A Story of the Near and Far Future as if they were separate books. I’ve corrected this.
Armytage in Yesterday’s Tomorrows: A Historical Survey of Future Societies, Routledge & Kegan Paul, 1968:
“‘When your writers romance of the future,’ writes one of the ‘last men’ in his Last and First Men (1930), ‘they too easily imagine a progress toward some kind of Utopia, in which beings like themselves live in unmitigated bliss among circumstances perfectly suited to a fixed human nature. I shall not describe any such paradise. Instead, I shall record huge fluctuations of joy and woe, the results of changes not only in man’s environment but in his fluid nature.’ The ‘huge fluctuations’, on Olaf Stapledon’s time-scale, cover 2,000 million years – nothing less than a history of man from his own time to the destruction of the solar system. In Last and First Men: A Story of the Near and Far Future (1930), Last Men in London (1932) and Star-Maker (1937), Stapledon carried Darwinian ideas far further than Wells. His method of dealing with the future was analogous to what Arnold Toynbee was currently doing for the past – envisaging the rise and fall of many civilisations – races and species even. Like Toynbee, Stapledon is concerned with unsuccessful attempts; like Marx, he was also concerned to show the dialectical reaction of one civilisation on another. Like Bernal he envisaged migrations from the earth to other planets, in Stapledon’s case first to Venus, then to Neptune, but having gone through mutations of the Bernal kind, his final eighteenth race, appearing millions of years from now, being recognisably human again.”