jamdonahoo ~ Actually the actors were trying to speak like Main Liners affecting what is known as the Main Line Malocclusion, a method of speaking with the teeth locked in place and articulating by lip movement. This is a minor variant of Locust Valley (Long Island) Lockjaw used by the yachting set in New York.
For the record, the British actors in this film are NOT trying to approximate the Greenwich (which is what I learned it as, or, as it is at other times called, "Locust Valley", or "Larchmont" - sources differ on the original locale to claim the accent, but they're all in that geographical area around Westchester Co., NY, L.I., NY and the So. Shore of Ct., where the affluent yachting set of Long Island Sound put in to port) Lockjaw. They are sounding British. There is no connection between the two, very different, accents.
Among the upper classes, and also for those who received training in speech, and this would apply to an era long before The Young Philadelphians, people would affect what was referred as correct, or stage, elocution. The net effect of that style of spoken language was a sound that was very similar to a formal, upper class, Southern England British accent in terms of the smartly clipped rhythm and cadence, without the vowel sounds that would make it sound all the way British. Billie Burke, being an old school actress from WAY back, would probably have learned to speak this way, and that is probably why some people would mistake her for being British. To my ear, she's a perfect example of that mode of speaking.
So, for that reason, British actors were able to find their places in films that required stuffy, upper-crust members of North-Eastern American society and that would go over with American audiences.
But, get your facts and your accents straight - the Larchmont Lockjaw and the "elocution" that sounds nearly British are two completely different sounds.