When Keira Knightley looks back on her latest movie, Official Secrets, it's likely to be intertwined with memories of her children. A year-and-a-half ago, she shot the film – a thrilling true story about British whistleblower Katharine Gun – in Liverpool, Manchester and across Yorkshire, just as her then three year-old daughter Edie was having 'a complete sleep-regression'.

It certainly didn't make things easy. 'The weeks when I had most of the work, she was literally up five or six times a night between midnight and 6am,' she explains. 'I think that added a particular vibe probably to my performance' – perhaps, the haggard, haunted look that hangs off Gun – 'which maybe I should thank her for or maybe I should blame it all on her for – I'm not quite sure!'

Now, holed up in London's Soho Hotel to promote the film, Knightley is just six weeks fresh from giving birth to Delilah, her second daughter with her musician husband James Righton. 'It's actually quite nice – I've suddenly stepped away from everything,' she says, referring to the fact she's barely read or watched any news reports in the run-up to Brexit whilst focusing on her new-born.

Yet banish any thoughts that Knightley is politically apathetic. 'I like being engaged in a discussion with the world around me,' she notes, 'and essentially that's what politics is.' For entertainment, she loves nothing more than something like Aaron Sorkin's The West Wing. So she jumped at the chance to play GCHQ translator Gun – who, in 2003, leaked a memo of US/UK plans to bribe UN Security Council members to vote for the impending Iraq war.

Knightley was just 17 then, and based in the States – where she was filming Pirates of the Caribbean, the film that turned her into a star. Still, having already been on one earlier anti-war march, she vividly remembers the demonstration on 15 February 2003 to stop the invasion of Iraq. 'I totally remember being on the phone to friends who were there.' For her generation, that shameful conflict 'shaped our world view of politics'.

Even so, Katharine Gun – who spent eight months on bail and narrowly escaped jail – was not someone she'd heard of. 'I just felt [her story] was a really interesting piece of this puzzle,' she says. They spent time together, leaving Knightley hugely impressed. 'She is very passionate still that it was the right thing to do. She's still outraged by politicians' actions. You feel that force from her very strongly and you feel she has a very strong sense of morality.'

Knightley read up on e-mails between the then Home Secretary Jack Straw and Prime Minister, Tony Blair, and how the public outcry was – for a time – making a difference. 'It was actually changing their minds,' she says. '[It shows] we shouldn't give up.' Good to her word, Knightley took her daughter Edie on the People's Vote march to demand a second referendum earlier this year. 'I think protestors are a very important part of democracy,' she says.

General release from Fri 18 Oct.