Why Did William F. Buckley Jr. Talk Like That?
An article in Slate sheds some light on it:
But if you listen to Buckley’s many debates—with Gore Vidal, Noam Chomsky, and others—the first thing you’ll notice is a distinctly British rhythm and melody. His pronunciation was likewise British-influenced in its lack of rhoticity—meaning he drops his “r”s. (An American “r” is generally pronounced with a tongue curled about 45 degrees; the Brits leave their tongues flat. Buckley is often somewhere in the middle.) This style of speech used to characterize upper-class New Englanders as a whole, since many of the region’s earliest settlers hailed from (old) England. (Fewer “r”s were dropped among the more diverse mix of immigrants in New York.) There’s also the yod, which is the “ew” sound in music and usual—like our friends across the pond, Buckley keeps the yod for words like news and pursue. He also pronounces the “t” in words like writer. And for vowels in words like thought and wrong, he rounded his lips, not unlike the English. Meanwhile, he stressed few words when he spoke but would pounce on an important one, every once in a while. (Contrast with John Wayne, who tended to stress every single word, in exactly the same way.)
Buckley Debates Chomsky: 1969