As mentioned in a previous answer to one of your questions, this is called [Mid-Atlantic English][1] and was commonly used in American films of the 1930s and 40s.

Wikipedia gives the following reasons that someone would use the accent:

 - Intentionally practiced for stage or other use (as with many Hollywood actors of the past). A version of this accent, codified by voice coach Edith Skinner, is widely taught in acting schools as American Theater Standard.  
 - Developed naturally by spending extended time in various Anglophone communities outside one's native environment, most typically in North America and the United Kingdom.  
 - Learned at a boarding school in America prior to the 1960s (after which it fell out of vogue).  

So essentially, this type of speech was never common and was only natural in the case of ex-pats.

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Some examples of 'Mid-Atlantic' speakers:

*Katherine Hepburn*  
Criticised for her shrill voice, she left Baltimore and studied with an acclaimed voice coach in New York City (Frances Robinson-Duff).

*Cary Grant*  
After moving to the United States, he managed to lose his accent, developing a clipped mid-Atlantic speaking style uniquely his own.

*Claude Rains*  
He grew up, according to his daughter, with "a very serious cockney accent and a speech impediment".  He had elocution lessons in Britain and then moved to America where he played British, American and European characters.

  [1]: http://en.wikipedia.org/wiki/Mid-Atlantic_English