Blunt, 33, said "Mary Poppins Returns" director Rob Marshall had a conversation with Andrews, now 80, who won the Academy Award for her performance as the magical nanny.
"Rob said he was in the Hamptons, and he saw (Andrews), and he said, 'It's top secret, but Emily Blunt's paying Mary Poppins'. And she went, 'Oh, wonderful!'," Blunt told the Entertainment Weekly.
"I felt like I wanted to cry. It was lovely to get her stamp of approval. That took the edge off it, for sure."
"I feel a little more trepidation with this [character] because she's so emblematic of people's nostalgia. It's such an important character in people's childhood," Blunt said while talking about the 1964 hit.
However, Blunt has a different take on Poppins than Andrews' interpretation of the character, first created by author PL Travers in a series of eight books.
"We're delving into the books a lot more, which is a different version of the character, I'll say that much. She's a little meaner, yeah.