On her visit, Knightley spoke to Rebecca Karkwasni, a 25-year-old mother of five, whose husband had been killed in a raid at a previous camp. "To the horrendous question 'What do you miss about your husband?', she said. 'I miss the way he holds me. I miss the way he makes my children laugh. I miss the way he makes me laugh. If I think about it too much my heart will break'," says Knightley, eyes swimming over again.
"We look at people in faraway countries, on television and we can't quite believe they are the same as us, but they are," she stresses. "They love their children as we do, they want an education for them, they want to give them a secure home and the freedom to run about in safety. Instead, they watch, powerless, as their toddlers play by the sewage - there's nowhere else for them."
Oxfam has drafted in Knightley to help shine a light on a benighted region that could head off a humanitarian disaster - but only if the rest of mankind helps them, and helps them immediately. It seems inevitable, if discomforting, that impassioned celebrity interventions will forever now be known as "doing an Angelina", after Angelina Jolie's milestone campaign to end rape as a weapon of war.
But, to her credit, Knightley is flattered, rather than piqued, by any such comparisons. "I admire Angelina Jolie hugely," she says. "I don't think I could ever be anything like as impressive or authoritative as she is on the world stage. She's pretty much devoting her life to her causes, and that's a great thing, a great message. I'm always happy to help in any small way I can."
But Knightley's reach in this sphere is greater than she might suppose. And when she speaks out - frivolously, about the strictures of a career lived in corsets, or gravely, about the war-torn and the traumatised - she has the credentials to make headlines.
Born to an actor father (Will Knightley) and playwright mother (Sharman Macdonald), she made her film debut aged 9, in A Village Affair. She has never been out of work since. From her Oscar-nominated performance in Pride and Prejudice, to the elegiac Atonement, her brittle, fever-bright Anna Karenina, and the satirical, knowing Pirates of the Caribbean franchise, she possesses a lambent radiance that fills the screen.
But in South Sudan nobody knew who she was. Nobody cared that she had won a Golden Globe and has graced the cover of Vogue many times and gets followed by photographers when she and her musician husband, James Righton, go out for an evening in the purlieus of west London.
"When those refugees asked me, 'Who are you?', I really, really wished I could have said, 'I'm a doctor', or something else useful," Knightley says quietly. "So instead I told them, 'I am somebody who is going to ask people to give lots of money to Oxfam, so they can help you'."
When we meet, Knightley is pale and jet-lagged. She wears no make-up on her fine-boned features and her hair falls free about her shoulders. She looks like a teenage ingenue; the very opposite of the poised, somewhat aloof Grace Kelly beauty she channels on red carpets. And yet in some respects her porcelain fragility today is every bit as mesmerising.
As attested by her recent appearance on The Graham Norton Show, when she and Samuel L Jackson riffed for almost an hour on the theme of no-show guest Jenson Button, there's an impish sense of very British humour beneath Knightley's A-list aura.
She even made fun of her extravagant pout in the Chanel adverts.
Knightley's figure was also perfect for that "career-making" green gown in Atonement - although at the mention of the phrase she flinches imperceptibly and swiftly interjects (half, but only half, jokingly): "I think you'll find I had a career before the dress, actually." There was, she adds, more than one frock, because she "kept trashing them". "The laser-cut edges were exquisite, but they couldn't withstand being ravished, especially not against a bookcase, so copies had to be made."
Having declared she was (temporarily) finished with costume dramas, as she wanted a break from faffing round in complicated wigs and underpinnings, Knightley's latest film is Begin Again, a soulful rom-com drama. The role proved challenging for a number of reasons, not least the requirement to play the guitar. Her husband of "one and a bit" years tried to teach her. The result (as anyone whose spouse has ever attempted to give them driving lessons could have predicted) was near carnage.
"I didn't hit him over the head with a guitar or set fire to my wedding dress, but I did feel consumed by a rage I'd never felt before," she says, sweetly. She learned enough to busk it (literally and metaphorically) in the film.
Knightley, who grew up in south-west London, identified her own dream from an early age. Around the point most little girls ask for a Barbie, she asked for her own agent - aged 3. By 9, she was keen to earn her living, but although she adored performing, initially her parents did all they could to put her off.
"My parents actively discouraged me from acting, until they found out I was dyslexic," smiles Knightley. "The school said you need to bribe her with something to make her apply herself, so the obvious incentive was acting. These days, I read slowly but I think fast - maybe that's what dyslexia is; we think a lot more than everybody else, which, when you think of it, is a gift, really."
It's a reflection of Knightley's self-acceptance - she has declared in the past that when she hit 25, she stopped caring so much what people thought - that she no longer gets exercised by commentators who probe her about weight matters.
"I once told an interviewer that my grandmother had anorexia in her teens. End of story. But the whole thing was blown out of such proportion that I heartily regret ever giving that information away. My mother's family are Scottish and tall and thin. So I don't get stressed about my size; it is what it is, I am the shape I am. There are more important matters in the world to worry about."
She is right, of course, and after a brief but significant pause, we return to them. The most pressing need in South Sudan is for clean water.
"What could be a more fundamental human need, a more fundamental human right, than water that won't make your children sick or kill your newborn baby?" asks Knightley. "In South Sudan they have nothing; the rains have just arrived, making disease more prevalent, and it's so much harder to reach those who need help most."
Knightley speaks of another refugee, Nyanyier Tuol Corker, aged 27, who lost her husband in the fighting and then two of her children to measles, a fatal hazard in the insanitary conditions of the camp.
"She told me, 'I want to die, but God won't let me. I have two children and I don't know how we are going to survive'," recounts Knightley. "How can we turn away from that sort of suffering?"
