In an interview this week, the actress spoke about the "embarrassing" moment she made a frank admission about her then-husband, actor James McAvoy, in conversation with the Duke of Cornwall.
The royal had asked about their relationship and how it works, given how busy they are with their respective careers.
Anne-Marie told The Guardian: "My most embarrassing moment involved Prince Charles. I was at a premiere with my ex-husband.
"Prince Charles said, 'I suppose you two never see each other'. I said, 'We see each other in bed'."
The actress plays hero Tracy Daszkiewicz as she leads the cast of the emotional BBC drama.
When her character experiences relationships on screen, many fans will have questions about the star's personal life off-screen.
For instance, why did Anne-Marie Duff and James McAvoy split and is she dating anyone now?
Here's everything you need to know...
Why did Anne-Marie Duff and James McAvoy split?
Anne-Marie and James were married for ten years and have one son together.
But in 2016, the couple announced that they were separating.
At the time, they released a statement, which read: "It is with tremendous sadness that we have come to the decision to divorce.
"We enter this next phase with continued friendship, love and respect for one another and the shared focus of caring for our son."
It continued: "We ask that you respect our and, most importantly, our child’s privacy during this time."
Anne-Marie discussed their break-up during an interview with the Times in 2018.
"Divorce is a profound, difficult experience. It just is. It’s a bit like you go to bed and you wake up holding hands in a hurricane. And nobody gave you any storm warnings,"she said.
"And if you are recognisable, you can’t leave the hurricane at home, because you walk down the street and everyone knows you are holding hands with the hurricane.
"They mean well and they are well-wishers, but they are strangers so you have to deal with that for a while and be as big a version of yourself as you can be."
What has James McAvoy said about the split?
James and Anne-Marie are extremely tight-lipped when it comes to their personal lives.
However, during an interview with Mr Porter magazine, he was asked about how he was coping following the break-up.
"My life has changed massively. At the same time so much has stayed the same," he said.
"One of the things that’s stayed the same is that I still don’t talk about my personal life, really."
James added: "Me and Anne-Marie, when we were together, it was our policy not to speak about each other in public. We rarely broke that and if we did, it was for tiny things – 'Yes, we are cooking turkey this Christmas' – and that policy still stands.
"Even separated, we're still respectful of each other and committed to doing that publicly and personally."
Who is Anne-Marie Duff dating now?
The Salisbury Poisonings star is thought to currently be single.
Since her divorce, the actress has been prioritising spending more time with her son Brendan.
Instead of taking on film and TV jobs, she signed up for stage work.
Anne-Marie told the Times: "(Theatre) also meant I could be with my boy. That’s a massive thing for me. It’s all about logistics when you’ve got a kid, isn’t it?
"Perhaps I needed to inhabit myself a bit more again."
Meanwhile, James is now in a relationship with production assistant Lisa Liberatti.
According to the Daily Mail, the couple secretly got married last year.
The couple confirmed their relationship on social media just months after his divorce was finalised.
- The Salisbury Poisonings continues on BBC One tonight at 9pm
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