When the Scandal box set dropped on to our mat, my partner took one look and said he'd be having an early night. Seven hours later we peeled ourselves away from the screen, having watched the entire series together back-to-back – but when I report this to Kerry Washington, she doesn't look surprised, just amused. "Yeah," she smiles, "I'm finding a lot of people telling me that. They watch it with their grandmother, or their girlfriend."

Now into its third series in the US, Scandal is the hit creation of Shonda Rhimes, who made Grey's Anatomy. Washington plays Olivia Pope, an elite crisis manager in Washington DC, part lawyer, part private eye, cop and political fixer – a tiny but formidable beauty in stilettos with a gift for getting what she wants out of everyone from foreign dictators to wealthy rapists to the president, with whom she has an on-off affair. Imagine Alastair Campbell and Matthew Freud in Naomi Campbell's body, and you begin to get the picture.

Pope is at once sympathetic and terrifying, and it's a measure of Washington's performance that she has to reassure me she's nothing like Pope in real life. "She's so much cooler than I am, so much smarter, so much more powerful, so much more fearless. I'm not going to tell you about yourself or try to manipulate you." She chuckles. "I'm definitely not her. She is based on a real-life person, though – and that person is pretty badass."

Pope is loosely based on Judy Smith, an African American crisis management expert who worked as a White House press secretary for George W Bush and has since advised clients from Monica Lewinsky to Wesley Snipes. She is still a crisis manager, but also a producer on the show. "So it's like, one week she's on set with us, the next she's in an undisclosed location doing work we can't know about." Washington has a conference call with Smith before filming each episode and the show's writers "come up with the most scandalous crisis situations they can think of, then say, 'Judy, what would you do? How would you fix that?'"

This helps explain why, despite the occasional far-fetched plotline and cartoonish cliche, Scandal feels so compelling. Even so, Washington hadn't even wanted to read the script when her agent suggested it. "I thought, a network TV drama? No way, no way. I have a thriving film career."

She's not being immodest: at 36, Washington is poised to make the breakthrough from interesting cinema actor to movie megastar. Her career began in television, with appearances in NYPD BlueBoston Legal and Law & Order, but soon graduated to cinema. Following roles in Mr & Mrs Smith and Spike Lee's She Hate Me, she played Idi Amin's wife in The Last King Of Scotland, Ray Charles' wife in the biopic Ray and Broomhilda, wife of the slave Django, in Quentin Tarantino's Django Unchained.