It’s dusk in the South Sudanese capital of Juba. A UN bus rolls over the dusty, pot-holed road as the Finnish former president Martti Ahtisaari, 75, shows monocle a picture on a Nokia smart-phone of his timber holiday cabin on a crystal-clear lake near Helsinki. It’s where most septuagenarians would choose to be in mid-summer.

Instead, Ahtisaari has just finished a gruelling 10-hour round trip to Batil refugee camp in the South Sudanese state of Upper Nile, home to a burgeoning population fleeing violence in the disputed border regions of Blue Nile and South Kordofan. Both he and his two blond security personnel look shattered.

“I am looking forward to being back home,” says the Nobel laureate and former UN special envoy for Kosovo, “[but] I do this because I feel I have a responsibility to use the experience I have. All conflicts can be solved.”

Ahtisaari is in formidable company. He is part of a delegation known as The Elders: an independent group of 10 global leaders formed by Nelson Mandela in 2007. They make up a diplomatic troupe of silver foxes that includes former UN secretary general Kofi Annan, one-time US president Jimmy Carter and Brazilian ex-president Fernando Henrique Cardoso, all set on abating conflicts and tackling some of the world’s most intractable problems.

The trip to South Sudan is led by the group’s chairman, Desmond Tutu, 81, the former archbishop of Cape Town and anti-apartheid champion (known affectionately as “Arch”) who sits up front poring over a typed list of his daily prayers. Behind him, Mary Robinson (the first female Irish president and one-time UN high commissioner for human rights) discusses the day’s events with the team’s policy experts. The excursion to the Batil camp follows a three-hour meeting with South Sudan president Salva Kiir. “I find it does help enormously with talks like these to see the situation first hand,” says Robinson. “These were very recent refugees affected by violence in Blue Nile. We were seeing old people, very young people and women. I could see the trauma in their faces. They have lived in one country that has become two and they should not have to flee in this way. This is no time for donor fatigue.”

Ex-presidents tend not to mince their words. Free from the constraints of office The Elders are frank, global interlocutors who use their collective experience to weigh in on issues from child marriage to long-running border disputes. The group’s fierce independence (they are funded by private donors including Richard Branson and Jeff Skoll) has given them the freedom to talk to some of the world’s pariahs. They sent a delegation to Pyongyang in 2011 and have engaged with Khaled Mashaal, the leader of Hamas, who has been stonewalled by most official diplomatic channels.

The group has also broken precedent in Sudan. Earlier this year President Carter and fellow Elder Lakhdar Brahimi (the former Algerian foreign affairs minister) went to Sudan to meet Omar al-Bashir, a man indicted by the International Criminal Court for crimes committed in Darfur.

“You have to remember I have known al-Bashir for almost 30 years,” Carter tells monocle during an interview in a London hotel. “I meet with him and he respects what I have to say. We had a list of things we wanted him to do. One of them was for the North Sudanese to withdraw their military forces from Abyei, a little territory on the border that’s been in the most intense dispute. While we were there he agreed to do so.”

Abyei is just one of the disputed border areas in South Sudan that has been wracked by violence. South Sudan has been independent for over a year yet the 2005 peace treaty that divided the two nations left many border demarcations unresolved and large swathes of Sudanese people displaced.

Khartoum accuses the government of South Sudan of supporting rebel force splm-North, which is fighting for territory in the area. Meanwhile, whole villages have been forced to flee aerial attacks and mob violence. (In Batil, monocle saw improvised bomb shelters made by children who still hide when an aircraft flies over.) The Elders’ mission is to edge on the peace process set out by an African Union panel chaired by South Africa’s president Thabo Mbeki. “Our role is to encourage the parties to get together for bilateral relations,” says Ahtisaari. “In my experience this is the only way we will see progress. There is currently no trade between the two countries but this must change. South Sudan and Sudan are symbiotic.”

The Elders work in parallel to the high-level negotiations they once led. Their style is subtle and often behind the scenes, using contacts and well-honed intuition to catalyse official processes. Their experiences of brokering peace are invaluable to this work. In Juba Tutu’s tenacious fight to free South Africa of apartheid, Ahtisaari’s role as a mediator in the Balkans and as the architect of Namibia’s independence are constantly cited as examples of successful outcomes. Former president Carter’s experience of hammering out the critical 1979 Camp David peace accords between Israel and Egypt is a benchmark of deft diplomatic negotiation and an agreement that still stands. “We don’t claim to have any authority except our moral authority,” says Carter. “When we speak privately to a leader about their human-rights abuses or the need for peace we think the gravitas of our collective background may have an impact.”

In diplomacy, kudos also counts for a lot. In Africa the mere presence of Desmond Tutu packs a punch; he is a powerful motivational speaker with a wry wit. “As you know, I have a hotline to heaven,” he tells a group of Unicef epidemiologists assembled in the Batil camp, “and I just had a call. You put a smile on God’s face. You have left comfortable homes to come here to help some of the most unfortunate people.” His words left many hardened aid workers in tears.

Age and stature allow The Elders to deliver blasts of indignation with impunity. While there are plenty of private meetings and subtle interventions in South Sudan, there are also a healthy number of public criticisms. On the final day of the visit at Juba’s Nyakuron Cultural Centre, Archbishop Tutu takes to the pulpit to praise God but also to lambast the new government for its failings. Just yards from Salva Kiir, who sits sweating in his trademark Stetson, Tutu’s sermon quickly moves from religious allegory to state-building. It is a searing call to the leader to take responsibility for the country’s development.

“I want to come back here and see roads, to see schools, to see tall buildings,” says Tutu. “South Sudan will never prosper unless there is peace.”

There is no talk of retirement in this circle. “I think that will be a decision that will be made by my doctors and by God’s will,” says Carter, who at 88 is the group’s oldest member and has come straight from a transatlantic flight to speak to the press in London. “As long as I’m able to actively pursue goals that are important to me, I’ll continue to do so.”