What accent did he have? It doesn't quite sound British, and it doesn't quite sound American. Was it an affectation? Was it a failed attempt at an American accent? Was it a now-obsolete accent, a la Mid-Atlantic? He was born in Lancashire and grew up in England and Scotland. He didn't arrive in the US until his mid-20s.
shareI think without having a shred of evidence to back it up that he exaggerated his usual speaking voice for comic effect. So it was probably his English accent as the base and worked up from there. He did tend to sound like a child, or a grown up speaking like a child might, or something like that.
He was born in Lancashire, but as was the custom, public figures back then were expected to develop a 'posh' accent.
I think he'd developed a general ''English accent'' but had lived in the US for a while- or sought to affect that as speaking roles came about.