To easily describe the Transatlantic accent is to describe it as old-timey or an accent from old new reels. The video above gives a pretty decent description/history of it. Interestingly, I came across this accent twice in the wild in my life. Once from a guy who admittedly has an auditory processing disorder, and then from a young Asian-American restauranteur who just talks that way.
As a side note, I once did customer support on the phones and talked to someone from Medford, Oregon. His accent sounded just like the exaggerated speech of a character proclaiming to be from that town over in the movie Double Indemnity from 1944.