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The movie, which was shown at the Venice film festival on Friday, is set over a weekend in the early 1990s when Diana joined the royal family for Christmas at the Queen’s Sandringham Estate.
The New York Times’ Kyle Buchanan said her casting was a “stroke of genius”.
He said: “Stewart is one of the few people on the planet who has known paparazzi scrutiny that is even somewhat comparable to the fusillade of flashbulbs that hounded Diana until her death.”
Screen Daily’s Jonathan Romney said the actress was “brittle, tender, sometimes playful and not a little uncanny”.
The Daily Telegraph’s Robbie Collin said she “will be instantly and justifiably awards-tipped for this”.
Speaking at a press conference at the film festival, Stewart told reporters: “I think my impression can only be my own. But Diana was a woman who wanted people to come together and I think that this movie’s ambition is to bridge gaps.
“I think if anyone ever made a movie about me, I wouldn’t feel like it was … I wouldn’t feel stolen from or taken from. There’s nothing salacious about our intention, I think that would be probably more embedded in interpretation.”
Describing the rules of royal life she had to learn, she said: “We had royal advisers, we had people to tell us all the things that you couldn’t know as an as an outsider.
“The stage that we depict in the film is a true unravelling.
“So, once I learned the curtsy and I learned that we are supposed not to go in the kitchen ourselves and steal food, all of those details, I don’t really remember them, but there was always someone around to make sure that if anything was out of line that we were remaining authentic and we weren’t undermining what we were trying to do, because obviously I’m American and not from that country.”