The question could be more broadly re-phrased as "When did Darwinian evolution become the scientific consensus?". Darwin noted the descent of vertebrates with lungs from fish with swim bladders:

I can, indeed, hardly doubt that all vertebrate animals having true lungs have descended by ordinary generation from an ancient prototype, of which we know nothing, furnished with a floating apparatus or swimbladder.

in his On the Origin of Species (1859). Haeckel's evolutionary trees showed the descent of other vertebrates from fish graphically:

• 1866: https://commons.wikimedia.org/wiki/File:Haeckel_arbol_bn.png

• 1877: https://commons.wikimedia.org/wiki/File:Human-evolution.jpg

In his 1866 tree, the Amphirrhina are the two-nostrilled vertebrates; the Monorhina which split from the tree just below are the jawless fishes (with one nostril), and thus the Amphirrhina are the jawed fishes until the branch that leads to Amphibia separates from the fishes. In his 1877 tree, Selachii (sharks) appear as the trunk supporting all of the jawed vertebrates (the jawless fishes branching off immediately below), and Dipneusta (lungfishes) ancestral to modern lungfishes and non-fish vertebrates with lungs.

While evolutionary ideas long predated Darwin, it was Darwin's work that quickly led to scientific acceptance of evolution, including descent of vertebrates from fishes. At least in Britain and Germany, the scientific consensus favoured evolution already in the 1870s, so this was nothing new by the time that Huxley wrote Brave New World. Aldous Huxley had a family connection with the scientific acceptance of evolution: his grandfather Thomas Huxley had been a famously-vocal advocate of Darwin's theory, "Darwin's bulldog", whose 1860 debate with Samuel Wilberforce is sometimes described as a turning point in the public and scientific acceptance of evolution.