Cary Grant is frequently cited as a prime example of that accent, though his was certainly a unique take on it. He spoke with an Americanised English accent, while it's usually the other way around.
It was, but it could be argued that that was what constituted a mid-Atlantic drawl.
I guess I have a different understanding of mid Atlantic.
I always assumed it was Virginia/Maryland/North Carolina.
I think of Betty Davis and Kate Hepburn as more New England/Northeast.
Dixie starts at Princeton, and proceeds south from there!
It well may be that the mid-Atlantic drawl now resides largely in the ear of the listener, but I think Dhaller may be essentially correct. It came in various flavors depending upon the locale in which it originated, surprisingly, often irrespective of latitude. Some mid-Atlantic drawls even came from new England.
A prime example might be William F. Buckley's Yale accent. One requirement of which is that one be able to speak without moving their upper lip -
And then we have my Uncle Arty. He was a graduate of that institution so often reviled by Buckley; Harvard. And the Harvard accent was also a mid-Atlantic drawl, but one different from that spoken by Mr. Buckley and other Yalies. It sounded more English, but an English accent that had been Americanized, and one not unlike Gary Grant's.
Sadly, my Uncle Arty only retained his Harvard accent when sober, and otherwise reverted to his dialect of origin, which I assure sounded nothing like Harvard.