Describing the pronunciation of Greek in schools in the UK, Allen says that a pamphlet by Arnold and Conway, "The Restored Pronunciation of Greek and Latin," pretty much set the standard that is still followed (link to 1907 version). The pamphlet came out in 1895, and there was a revision in 1908, which is available on libgen.rs. In the 1908 version, they seem to have backed off on the pronunciation of θ, φ, and χ.
The proposals that we made in 1895 have passed through the test of practice, and have in the main been found feasible. Difficulty, however, is attached to insistence on the 'narrow' pronunciation of ει, the 'broad' pronunciation of ω, and the pure 'aspirate' values of θ, φ, χ. In the present edition we have thought it well to allow a certain latitude in the pronunciation of ει and ω, and we have taken a new departure with regard to the 'aspirates.' Some recently discovered evidence [referring to an appendix] has made it probable that the pronunciation of these sounds had become, in part at least, that of fricatives as early as the fourth century B.C...
<editorial>The whole premise seems a little absurd to me, since these people never even seem to feel that it's necessary to justify the privileging of a particular time and place over the use of another dialect, such as Homeric, koine, or modern Greek. For that matter, I think some justification is needed for the premise that we should not just adopt an arbitrary coding of the phonemes into something convenient for our own mouths and brains. The gee-whiz historical claims sound to me like they're probably more of a fig leaf for the fact that the reconstructed pronunciation of θ, φ, and χ was a massive failure educationally, since English speakers can't easily hear and produce the relevant distinctions.</editorial>
But in any case, did the "recently discovered evidence" actually pan out?