Though not Cockney, Keanu Reeves certainly defeated Van Dyke in silliest UK accents playing Harker in Dracula. Haven't seen Costner's Robin Hood, but shouldn't they have been speaking French, given the period?
I've always believed Mary Poppins to be Disney's best live action & perhaps best all around film. Though I agree with Travers that the animation scenes really didn't belong. I haven't read up on the issue, but was it that Disney believed animation was necessary because it was the studio's trademark?