James plays the younger version of Streep’s character Donna in Mamma Mia: Here We Go Again, which is out today.
Speaking to Jimmy Fallon on his US chatshow, James revealed the moment she came face-to-face with her idol – whilst crying.
“When I met her [on set] – she’s the greatest actor ever – she was singing a song and it was in a chapel and it was so beautiful and I was crying,” she said.
“They were like, ‘you’re about to meet her’, and I was like, ‘oh God’.”
The chapel sequence, which has been teased by other stars, comes near the end of the movie – and sees Streep duetting with on-screen daughter Amanda Seyfried.
Seyfried appeared on Fallon’s show one day after James and said she thinks the sequel is better than its predecessor.
“I’m so excited for everyone to see it,” she beamed.
“It’s so much better than the first one, and I can’t believe I’m saying that.
“If the first one was a beach, this one is an ocean. I’m talking about depth here!
“And you might think I’m kidding but I’m not, it’s so emotionally deep and beautiful.”
Mamma Mia: Here We Go Again has had positive reviews from critics, including a four-star critique from Express.co.uk.
Alongside Streep, James and Seyfried are returning stars Christine Baranski, Julie Walters, Pierce Brosnan, Colin Firth, Dominic Cooper and Stellan Skarsgard.
Cher is also on board as Ruby Sheridan; the grandmother of Seyfried’s Sophie and mother of Donna.
Mamma Mia: Here We Go Again is out now.