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"We were rehearsing a scene where she plays a witch and she was supposed to jump on the table with her cape and everything, and I saw it happening in slow motion...
Meryl Streep and Emily Blunt in Into The Woods
Emily, who was pregnant with her first child during filming, added: "Rob Marshall [the director] and James Corden froze, and the pregnant women caught her.
"I actually caught her, so she owes me, big time."
Earlier in the interview, Emily had discussed starring alongside Meryl in Into The Woods, and The Devil Wears Prada, and joked: "She's so amazing, it's annoying. She was tormenting me in that, and now she's tormenting me in this movie.
Emily Blunt with Meryl Streep and Anne Hathaway in The Devil Wears Prada
"I said, 'This is it, we can't have any other dynamic now, you have to hate me.'"
Into The Woods begins with the Baker and the Baker's wife, plated by James and Emily, and their interaction with the evil old witch, Meryl, who has placed a curse of the couple, leaving them childless.
Soon Cinderella (Anna Kendrick), Little Red Riding Hood (Lilla Crawford), Jack and the Beanstalk (Daniel Huttlestone), and Rapunzel (MacKenzie Mauzy) all become bound together with the couple, as they attempt to break the witch's spell.
Also starring Johnny Depp as the Big Bad Wolf and Chris Pine as Prince Charming, Into The Woods is out in the UK on January 9 2015.