I would not call that British. It sounds like old-fashioned New England to me. I have watched enough movies made in the 1930s to know that until WWII, Americans aspired to a British-type accent as closer to ideal.
The generic Mid-western “newscaster” accent had not developed yet, and people who wanted to progress as speakers in the US needed to incorporate this sound to an extent into their speech. Walter Cronkite was born in Missouri, and lived in Texas for a portion of his childhood, but he obviously had effected speech. (Or affected, if you prefer, but I meant to say “deliberately chosen.”) By the time he was “The most trusted man in America,” his speech was his own, and natural for him, but it was not the accent he would have had if he’d been a bricklayer or linotypist.
Another really interesting showpiece in the category of “effected” accents on American English is Helen Keller. She grew up in Tuscumbia, Alabama, but when she learned to speak, it was not in the US south. It was from a speech therapist who was all New England, and probably affected to a degree herself, even beyond what her upbringing implied. Keller’s speech is very hard to understand, and yet her New England vowels are unmistakable.
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But to return to Eleanor Roosevelt-- it’s not enough to say that because an accent has elongated vowels, or is rhotic, that it is “British.” It needs to be identified with a geographical region to be truly British. Otherwise, it’s just a rhotic accent with elongated vowels, typical of many British and New England accents both.
It may be that in 2020, Eleanor Roosevelt’s accent sounds “British” to us, but I think in her own time, that was not true. I lived in New York as a child, as was around Connecticut, and other areas of New England frequently, then, when I was 10, I went to an international school, where I had a teacher who was from England (exactly where, I’m not sure, but I do know she was English, not Scottish, Welsh or Irish), and a very good friend from London, and was surrounded by children with a host of different accents.
You can’t always judge the proximity of acquisition by whether two accents sound similar. There are areas of Scotland where people sound very English, but they are not necessarily border regions-- and some border regions where the accent is extremely difficult for Americans to understand.
By the same token, eastern US accents vary considerably. There are areas of Connecticut that are served by the Greater New York transit system, but they don’t share the distinct qualities that mark the accents of New York City. No matter what part of Connecticut people are from, they tend to sound like New Englanders. As for New York, though, people upstate often have a very generic US accent. You won’t place them in the south, or in some place with a distinctive regional dialect like Minnesota, but people from western New York state, and people from northern Ohio can be hard to tell apart.
At any rate, the New England accent, the natural one, leaving aside the received accent for the moment, has changed considerably from Eleanor Roosevelt’s time.
I don’t know how old the OP is, but I was born in 1967, and I very well remember old New Englanders and the way they spoke in my childhood. Eleanor Roosevelt sounds pretty much like one of them. But I don’t hear that speech from anyone living anymore.
I think she spoke an American accent-- maybe not a widespread one, but definitely an American one; however, one that no longer exists. I think there may have been some deliberate imitation of British-style vowels in it, which were no longer considered necessary after WWII, when speaking more obviously like an American was suddenly OK.
