"For our own sanity, and actually for the benefit of the relationship, we had very clear boundaries," Anderson tells Harper's Bazaar about the delicate process of stepping into the heels of former British Prime Minister Margaret Thatcher.
Eventually, the couple settled on the very simple rule, "I am not going to comment on the script, but you are not allowed to comment on the performance!" says Anderson, 52.
"I’m pretty good at compartmentalizing in my life, period,” she adds.
"I think I learnt that quite young, being a young mother, in a really intense TV series where it was either full-on on-set, or I was in my trailer having to shut the door and no longer be that person but be Mum."
For Anderson – who is mom to Piper, 26, Oscar, 14, and Felix, 12 – this rule also applied to her portrayal of Thatcher, who was nicknamed "The Iron Lady" because of her tough and often unpopular tenure at No.10 Downing Street.
To capture the character, Anderson says she first had to push her own personal opinions to one side.
“I had to get to a point where it’s nothing to do with my opinions of her policies, of her actions,” she tells Harper’s Bazaar.
The result, says Anderson, is that her portrayal is “only about her as a human being and her motivation as a politician and as a mother."
Watch: How Gillian Anderson became Margaret Thatcher
A trailer released on Oct.29 shows the monarch (portrayed by Olivia Colman) looking forward to having a female prime minister, only for their relations to rapidly sour.
"I think we have enough respect for one another personally to ask ourselves some of the bigger questions, woman to woman," the prime minister is heard challenging the queen in a voiceover narration.
The royal then warns Thatcher to not make enemies "left, right and center," only for the politician to reply that she's more than comfortable with having multiple adversaries.
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While Anderson looks every inch a clone of Thatcher in her replica power costume of a business suit, pearl necklace and bouffant hairstyle, this is a political style that doesn't sit so easily with the actor away from the screen.
“I feel like I have an opportunity as somebody in the public eye to draw attention to things, but I don’t comment, I don’t offer my opinion on social media on a regular basis," Anderson tells Harper's Bazaar.
"It’s not my world. I’m an actor, I’m not a politician, I’m not a social worker.”
Watch: Diana's designer recalls her famous debut and that little black dress