The Oscar-winning star is taking on the role of the former British Prime Minister in the film, which is set to be released on January 6 next year.
Speaking about how Streep got the voice so spot on, producer Damian Jones said to UK newspaper Daily Mail: 'You're talking about the best actress in the world. She did it herself.
'She went deep inside Mrs Thatcher to do it. And you have to remember that the real Mrs Thatcher's voice was different before Gordon Reece did his makeover when she became leader. Her clothes, her look and her voice changed.'
He added: 'Meryl had to learn the speech pattern she had and then master how the voice became. She went on YouTube and found every bit of footage that featured Thatcher speaking.'