Loved and loathed, she's been played by everyone from Gillian Anderson to Meryl Streep, and cited as an idol for incoming Prime Minister Liz Truss.
But how do you tackle playing Margaret Thatcher?
"Definitely the wig and the shoes came later," says Kate Fahy, who is reprising the role in a revival of Handbagged at Kiln Theatre.
"Before that there is the voice - and not just the voice, the whole approach. I didn't watch the other Thatchers, but I watched a lot of YouTube including a Swedish chat show where she bossily takes the host to task about Sweden's tax rate!
"When I finally got the wig I thought 'thank God, my job is done, just send the wig on.'"
When first approached to play the Iron Lady, Fahy's initial thought was 'crikey I am nothing like her'
"Then I read the script and thought 'I could have so much fun here'. It may be that because so many people have played her, you are slightly off the hook."
Moira Buffini's political satire pitches an older Thatcher and the monarch looking back on their younger selves.
"It's a contest between Margaret Thatcher and the Queen, competing for ownership of what went on in their private audiences - and I can tell you straight up the Queen wins. Margaret Thatcher is very much the baddie in the piece ."
Inspired by the women's shared love of Launer handbags, Buffini's play imagines their differences and arguments; over sanctions against South Africa, Rhodesia's move to democracy; and using the Police as an army to crush strikes and protests.
"Although she has created their private conversations, almost every line that I say, Margaret Thatcher actually said," says Fahy.
With two actors playing a younger M and Q, and two men playing 27 other characters, she adds: "It's very fast moving, sharp and funny with people popping on and off - a bit tight-ropey for us."
As for her own feelings about Thatcher, the Dublin born-actor said: "I lived through the Thatcher years, and know it all. She polarised people - they either loved or loathed her. Loathing was my feeling, but as an actor you don't want to take any view on her. If you are playing Hitler you have to find the character's inner workings - not make them look better or worse, just be truthful. Moira has written a fantastic play in which her point is made, and I am part of a group of people realising it."
Hindsight has made Fahy view her "commitment and unwillingness to bend to what was expedient" in a fresh light.
"Given the last three years under Boris Johnson even I can say at least she had honour and believed it, instead of just wanting the next promotion. She said herself in interviews she was not interested in negotiation or consensus. 'When you have firm principles you know what is right.' The problem was in the end she wouldn't listen to anyone, it was a one person government."
Fahy, who lived in Highgate for two decades with partner Jonathan Pryce before moving to central London when their children had grown, said while touring Handbagged in 2014, the play was a political bellwether.
"You really knew where you were. In Canterbury people are fond of Margaret Thatcher, in Salford I got booed, and in Edinburgh they don't much like The Queen or Margaret Thatcher. In Washington they loved it, but New York didn't get it much at all.
"Having an opportunity to do it again is a bonus. A lot of talk since Boris resigned has referred to Thatcher's politics and style; Liz Truss has touted her as one of her great idols. That era was the beginning of where we are now; deregulation, privatisation. You hear lines differently, it's more relevant now than ever."
Handbagged runs at Kiln Theatre, Kilburn from September 9-October 22. kilntheatre.com
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