So I did a regressions of the growth rate in each period on the log of per-capita GDP at the start of the period and a dummy variable for English speaking countries:
g5080=5.30-.499 lgdp50 - .212 English
g8010=3.64-.333 lgdp89 + .104 English
The coefficient on English in the first regression is highly statistically significant at conventional levels (t=3.7), while the coefficient in the second is borderline (t=1.95). The difference between the estimates is highly significant (t=4.3). The big developments of the second period include globalization and the growth of the financial sector, and since English is the language of international business, it seems possible that having an English-speaking population really contributed to growth in that period. It's hard to imagine why being English-speaking would be a negative factor in the first period, but all of the English-speaking countries have similarities in legal and political systems and possibly in culture, and maybe some of those factors affected economic performance.