And yet a question arises: very few of the Sweeney Todd cast did English accents, as you say. Cariou didn't. Lyndeck. Many of the chorus. Sarah Rice. Ken Jennings.
And yet somehow, because of the somewhat Brechtian feeling of the show, it didn't matter to the effect. I have often wondered about Todd's accent if the character were meant to be real: he would probably be cockney; which accent would sit poorly on Sondheim's Romantic lyrics. His accent on Broadway was classless and regionless by English standards.
As you say, only Lansbury was doing the real deal when it came to accent.
And yet, as I say, it mattered not a jot. The original cast and production - and orchestrations! - were overwhelming. Nothing quite comes near it, before or since - certainly no revival of it.