Streep has adopted Thatcher's trademark bouffant hairstyle, ruby-red lipstick and pearl earrings for her part in the film about Britain's longest continuously serving premier of the 20th century.
"The prospect of exploring the swathe cut through history by this remarkable woman is a daunting and exciting challenge," said Streep, in a statement from the film's producers.
"I am trying to approach the role with as much zeal, fervour and attention to detail as the real Lady Thatcher possesses. I can only hope my stamina will begin to approach her own," she added.
The movie, due for release later this year, reunites Streep with "Mamma Mia!" director Phyllida Lloyd and also stars veteran British actor Jim Broadbent as Thatcher's husband Denis.
The script for the film, which began shooting at the end of January, covers a broad sweep of Thatcher's career.
Pathe, which is producing the movie with Film4 and the UK Film Council, said it is about "a woman who smashed through the barriers of gender and class to be heard in a male dominated world."
Thatcher, whose nickname gives the film its title, is the only woman ever to be the British prime minister.
In power at the head of a Conservative government from 1979 to 1990, she oversaw a transformation of the British economy but crushed the trade unions and took Britain into a brief war to retake the Falkland Islands from Argentinean forces.
The increasingly frail ex-leader, who is now 85, has suffered a series of minor strokes since leaving office and was told by doctors to quit public speaking in 2002. She spent two weeks in a hospital late last year after being admitted with flu.
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