A free, accessible exhibition about Nelson Mandela, marking what would have been his 100th birthday, is such an indisputably good thing, it seems mean-spirited to even try to assess it critically, as if to do so were to take issue with the South African figurehead himself.

Mandela is the model of a wise, benign, dignified statesman, and the world could certainly do with more of those right now. Barack Obama pointed this out last week in Johannesburg. Giving the annual Mandela lecture, he contrasted the progressive democratic triumphs of the 1990s – such as South Africa and the collapse of the Soviet Union – with the present climate of tribalism, resentment and “strongman politics”. Addressing Mandela by his clan name, he said: “We have to follow Madiba’s example of persistence and of hope.”

Those looking to do so will find ample inspiration and ammunition at this show, even if the presentation is somewhat dry and dutiful. This is primarily a two-dimensional exhibition of text and photographic images, neatly designed and laid out across six walkaround clusters of wall-sized panels, huddled together in the cavernous semi-cafe space of the Purcell Room.

Inspiration … the Centenary Exhibition at the Southbank Centre. Photograph: Pete Woodhead

Distilling a life as storied as Mandela’s into digestible chunks is a daunting task, but it has been done judiciously, combining biography with political context, plus personal episodes and anecdotes. Each set of panels addresses a phase of Mandela’s life and persona: character, comrade, leader, prisoner, negotiator, statesman.

It is a story of rags to riches. The beginning “character” section includes Mandela’s recollection of donning his first pair of trousers – a novelty for a 1920s South African village boy – to go to school. His father simply put him in a pair of his own trousers, cut them at the knee and tied them with string.

From there, the story progresses through Mandela’s political awakening, his organised resistance to the apartheid regime and deepening involvement with the African National Congress, imprisonment for 27 years, and eventual release and election as South Africa’s first black president.

‘It’s the details that stick in the mind’ … Mandela in 2006. Photograph: Kim Ludbrook/EPA

It is often the small personal details that stick in the mind. In a 1976 letter to his wife Winnie, Mandela writes how he carefully dusts her photograph in his cell every morning. “I sometimes touch your nose with mine to recapture that electric current that used to flash through my body whenever I did so.” Or the fact that the Robben Island prison, where Mandela was sent in 1964, did not have hot water until 1973.

But care is also taken to illustrate how Mandela’s experiences shaped him as a leader. Desmond Tutu observes, for example, that during Mandela’s decades in prison, “suffering deepened his spiritual resource, and he grew in that time in magnanimity and generosity of spirit”. There is a bracing clip of Mandela giving his first television interview, to ITN in 1961, where he calmly and eloquently outlines why he will not renounce the use of violence so long as the white authorities continue to use it against him and his people.

And there are stories of Mandela charming his adversaries, gaining their respect, engaging with them constructively, working not towards goals of “victory” or “revolution” but peaceable, sustainable reconciliation. The latter, as much as anything in Mandela’s life, seems like a quality in lamentably short supply right now.

One weakness of this exhibition is the lack of local specificity. Put together by Johannesburg’s Apartheid Museum, this is a generic touring show that has already travelled to other major cities, including Paris and Dublin. When the Duke and Duchess of Sussex visited last week, alongside former inmates of Robben Island, and Mandela’s granddaughter Zamaswazi Dlamini-Mandela, there was much talk of Mandela’s connections with Britain. He first visited London in 1962 and returned many times, meeting everyone from the parents of Stephen Lawrence to Naomi Campbell.

The Duke and Duchess of Sussex at the exhibition. Photograph: Arthur Edwards/AFP/Getty

According to Zindzi Mandela, his daughter, he was such good friends with the Queen, he called her “Lizzie”. London also became the home of South African political exiles such as Oliver Tambo, as well as the epicentre of the global anti-apartheid movement. You could also argue that as South Africa’s former colonial oppressor, Britain was responsible for much of the injustice Mandela had to overcome in the first place. None of these aspects are addressed here.

There is a display of anti-apartheid ephemera lurking near the back but it feels like an afterthought. A pity, as it contains some vibrantly designed posters for marches, protests and consumer boycotts, plus a handwritten letter in which Mandela thanks “the British public” for their “overwhelming generosity”, written on the day of the Mandela Freedom Concert at Wembley Stadium in April 1990.

But this really is free Nelson Mandela, and this exhibition accomplishes its primary mission of communicating his remarkable story faithfully to as wide an audience as possible. Whether you drop in for a 10-minute browse or spend an hour reading every caption, it will be time well spent. The more future Mandelas it inspires, the better.