Streep plays the former prime minister in Phyllida Lloyd's The Iron Lady, while Peep Show star Colman plays her daughter Carol.
Asked what it was like to work with Streep, Colman told Stylist: "It was amazing. I love her!
"To sit in a room with her, well, I couldn't quite believe it. She's very close to giggles all the time."
Asked if she had to 'prove something' in new movie Tyrannosaur, Colman said: "Maybe. [Director] Paddy Considine has thrown me a rope, he really has. I'll never know why he let me do it.
"I don't have anything on paper to show it was a good gamble. Paddy is like magic - he sees into your soul."
> Meryl Streep as Margaret Thatcher in 'The Iron Lady' - first poster
Watch a trailer for Tyrannosaur below