In the documentary Wishful Drinking , Carrie Fisher brings up her changing accent.
It was because she was going to school in Britain
and she picked up some of the local accent.
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I had never noticed that before, but it would fit the story.
The pseudo-British accent is heard coming from just about every character that is a part of the Empire.
At the beginning of episode IV Leia is still attempting to act undercover as part of a "diplomatic mission".
Once out of the undercover environment, and safely around the resistance, her speaking would shift back towards the more American accent used by most of the rebels.
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In-universe, the British accent is called Coruscanti , and it was often adopted to give the speaker an air of authority and/or political legitimacy during the days of the Empire.
The difference in Leia's accent is referenced in the novel Backlash by Aaron Allston.
In the excerpt below, two Imperials are watching a holo-recording recovered from the first Death Star, one taken moments before the destruction of Alderaan:
Senator Leia surged forward.
Her body language, the little of it that could be seen, was one of entreaty, pleading.
When she spoke, her voice was not quite right, not quite the voice
Lecersen had been familiar with for many years.
Its pitch was a touch higher, and it carried the clipped tones of the Coruscanti accent, nearly identical to Tarkin's, that so many Senators and other politicians affected back in the days of the Empire, even when they were not from Coruscant.
"
No.
Alderaan is peaceful.
We have no weapons.
You can't possibly—" Tarkin's voice turned harsh, commanding.
"You would prefer another target?
A military target?
Then name the system!"
Out-of-universe, as explained in the accepted answer, actress Carrie Fisher had been living in England and adopted a British accent prior to shooting, and gradually lost it during production.
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In universe, the newly canonical explanation is provided in Bloodline : according to this book, Leia spoke that way to mock Tarkin.
Casterfo had the same sort of aristocratic accent Grand Moff Tarkin had spoken in, the one so many senior Imperial officers affected, the one she’d mocked when she and Tarkin last stood face-to-face.
- Star Wars: Journey to the Force Awakens: Bloodline , by Claudia Gray
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Leia grew up as a princess on Alderaan, which as we all knew developed an accent similar to our "British" accent.
But when the evil Lord Vader blew that planet up all traces of that accent were wiped out from the universe save for the few fledging survivors that were scattered throughout the universe at the time.
And since in the Star Wars universe, traits of the people are only able to carry when there is a large group of people to carry those traits, all learned traits of Alderaan vanished with the planet.
So after the planet was destroyed the accent slipped away from Leia like the other traits of Alderaan (of which I'm sure she didn't miss: the propensity to hoard, be extremely frugal, and get really sad when it rains of a Tuesday.
Also a strong desire to eat meat.).
And since she was a mixed native of Tatooine and Naboo, those inherent traits came back (less bun-hair, more hardass, also a desire for incest, strangely enough).
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It's well documented that David Prowse was doing a voice for Darth Vader at the time, but that his west-country accent made him more "Darth Farmer" than "Darth Vader".
It wouldn't surprise me if you could heard the occasional west-country accent coming through any of the actors.
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In Episode IV, Carrie Fisher pronounces Han Solo's first name as if he were the leader of the Han Dynasty.
In Episode V, she picks up Billy Dee Williams' accent and pronounces "Han" as to rhyme with Peter "Pan."
In Episode VI, she's back to the Han Dynasty.
I think she picks up the accents of those she hears the most (as do we all).
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In the first 30 minutes of Star Wars IV, Leia has a pseudo-British accent.  As the movie progresses she loses her accent and gets a more American-tough girl accent.  Is there a reason behind this?
Why does Leia's accent change during A New Hope?
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<star-wars><a-new-hope><accent>
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 In-universe, the British accent is called  Coruscanti , and it was often adopted to give the speaker an air of authority and/or political legitimacy during the days of the Empire. When Alderaan was blown up by Vader, most traces of that accent were wiped out, apart from a few survivors. Out-of-universe, actress  Carrie Fisher  had been living in England and adopted a British accent prior to shooting, and gradually lost it during production. Leia's accent has roots both in and out-of-universe. In-universe, she grew up with a Coruscanti accent and lost it when the planet was blown up. Out-of-universe, the actress who played Leia had spent time in England and picked up a British accent.
In-universe, the British accent is called Coruscanti and was used to give an air of authority. Leia was a princess of Alderaan and grew up with that accent. However, the accent was lost when the planet was blown up by Lord Vader. Leia's accent is referenced in the novel "Backlash" by Aaron Allston.  Out-of-universe, Carri Fisher, the actress who played Leia had been living in England and picked up a British accent.