“Don’t you hear the H-bomb’s thunder / Echo like the crack of doom?” This song is painful as well as rousing when heard now on film footage of the first Aldermaston marches of 1958 and 1959; they look like a vision of lost innocence. This is partly on account of the wholesome quality of their participants: girls in duffel coats, babies in Victorian-looking prams, fresh-faced boys playing their guitars. Even the police seem unusually helpful, ushering demonstrators into position in Trafalgar Square, where a young woman energetically conducts her choir. But if watching these scenes induces a feeling of sad nostalgia then it’s primarily because of the optimism on display.

And at such a dangerous time. “Four minutes warning – just time to boil your last egg,” reads one placard. The fear was real. What seems different from now is their belief that the pictures of mushroom clouds are so self-evidently horrible that merely displaying them would have some effect. As one protester, Hugh Jenkins, recently recalled: “Things in those days were simple and straightforward … we simply said ‘Ban the bomb!’ We thought if we got public support we’d make it clear to the government that the world did not want weapons of such mass destruction.”

Aldermaston is one of the many protests documented in a new exhibition, People Power: Fighting for Peace, at London’s Imperial War Museum, tracing the history of anti-war demonstration since the beginning of the 20th century. The exhibition starts with the conscientious objectors of the first world war before commemorating the 1930s pacifists and their divided responses to nazism. It then enters the cold war era, when protests became more focused on the survival of mankind in general than on specific wars, though some attention here is given to the demonstrations against Vietnam. The final rooms document the more recent protests against the western interventions in the Middle East, notably the wars in Iraq.

Facebook Twitter Pinterest ‘Bitter truths to burn their lousy souls’ … Wire by Paul Nash (1918). Photograph: IWM/Paul Nash

If Aldermaston emerges as an unusually optimistic moment it’s because it has since become clear that protests have less effect than Jenkins and his comrades anticipated. Some of the exhibition’s most moving works take us back to the women’s camp at Greenham Common in the 1980s. Yet two years after the camp started as a protest against the nuclear weapons being sited there, the cruise missiles arrived, causing some protesters to lose hope.

The exhibition makes good use of Ernest Rodker, the young activist rather unfairly immortalised as Tommy in Doris Lessing’s The Golden Notebook, who marched at Aldermaston and later marched in February 2003, when a crowd of 2 million gathered in London to demonstrate against the proposed war in Iraq. In an interview for the museum’s show, he echoes the thoughts of those who thought “this is going to have an impact” and were disillusioned when it didn’t. “Many people thought ‘What’s the point?’ The biggest march that had ever been and no impact, just ignored by Blair.”

Yet the exhibition is timely, because now we are on the march again. I’m part of a large cohort who hadn’t marched since the despair of 2003, but took to the streets once more for the Women’s March in January. As causes of outrage proliferate, I can see that I’ll be marching again before the year is out. Though I can’t share the optimism of the eager crowds leaving Aldermaston, I have lost some of the hopelessness I felt in the wake of the Iraq march, if only because in Trump we have an opponent who at least seems to care about the size of the crowds that turn out.

Facebook Twitter Pinterest Haunting … Kennard’s 1981 work in full Photograph: ©Peter Kennard

So now is a good moment to think about how protest works and what it can achieve. And it’s clear from the works on display that the Women’s March has a long and distinguished lineage of collective female protest, from the “peacettes” of the first world war to the Women’s International League for Peace and Freedom (founded in 1915 and still active today) to the women of Greenham Common. “As a woman I have no country,” wrote Virginia Woolf on the eve of the second world war, convinced that women were going to find it easier than men to rid themselves of the “pride of nationality” and the presumed “superiority of patriotism”.

This is largely a social history exhibition. There are armbands, first aid certificates and letters of disgust (“you dirty sniffling coward – don’t dare to call yourself British,” one second world war conchie was informed); there is an accordion and a purple cotton jumpsuit. But the curators have chosen to include some works of art alongside the artefacts, which raises questions about the relationship between art and protest.

According to Adorno, “every work of art is an uncommitted crime”, meaning that art by definition challenges the status quo. Some artists, though, engage more directly with politics than others, and these seem to fall into two camps. In the first group are those, such as Paul Nash, who have responded antagonistically to war in the abstract. “I am no longer an artist interested [and] curious,” he wrote to his wife from the front in 1917; “I am a messenger who will bring back word from men fighting to those who want the war to go on forever. Feeble, inarticulate, will be my message, but it will have a bitter truth and may it burn their lousy souls.”

Facebook Twitter Pinterest Ban the bomb with baby … nuclear protesters in Trafalgar Square in1958. Photograph: Fred Ramage/Getty

He chose to deliver this message through paintings that took his experiences of war and turned them into something too universal to be simply protest art. In Wire (1918) he used the brutality of barbed wire to turn the landscape of the trenches into an apocalyptic world.

This tradition is continued today by Maggi Hambling, whose absence from the exhibition feels like an omission. Since the Falklands war, Hambling has been painting violence with passionate fury, but her most powerful images are abstract. In a recent series entitled Victim made as a response to Benjamin Britten’s War Requiem, she evokes ambiguously corporeal figures within swirls of destruction that seem to show the body at the moment of dissolution.

While Hambling condemns war, she also acknowledges its seduction, and there is no clear moral message in these pictures. “War is inside us all,” she writes; “we can’t deny it, even if I’ve never actually wanted to kill anyone.” This is a different approach from the other camp of artists – those who engage more directly in political protest, who are more prominently featured in this exhibition.

Facebook Twitter Pinterest Photo Op by kennardphillipps (2005). Photograph: IWM/© kennardphillipps

Prominent space is given to Peter Kennard and Cat Phillipps’s 2005 Photo Op, showing Blair apparently taking a selfie in front of a burning oilfield in Iraq. The artists describe their satirical work as “the visual arm of protest”. This approach is shared by Banksy, refreshingly not included in this exhibition, and Richard Hamilton, whose Shock and Awe garbed Blair in wild west attire, stepping over a rough terrain that was actually an enlarged image of a swirl of oil paint.

Placed alongside the badges and armbands, Kennard and Phillipps’s picture feels too polished. This is protest designed for the gallery, and yet, in this space, there’s only so far it can take us. It’s the homemade quality of the Aldermaston and Greenham Common protests that is moving: those carefully drawn or sewn banners, some of which are included here. At Greenham, women decorated the entire eight-mile perimeter of the base with photographs, flowers and the occasional dinner service – what Kennard has described as “one of the greatest art works of the 20th century”.

If he is right, then protest art may be more powerful outside the gallery: when it doesn’t know it’s art. Kennard has straddled these two areas, making posters that are designed to make a statement. His Protest and Survive (1980) showed a skeleton reading the official booklet, Protect and Survive, on protection against nuclear attacks. This image still makes an impact, as does FHK Henrion’s CND poster showing a skeleton blending into a mushroom cloud under the heading “Stop Nuclear Suicide”. But these pictures began as protest propaganda rather than as art.

The best test case for the distinction between accidental and intentional art is Brian Haw’s Parliament Square protest camp, set up in 2001 and recreated at Tate Britain by Mark Wallinger in his Turner prize-winning State Britain (2007). It’s sensible, I think, that the Imperial War Museum has chosen to use Haw’s original materials, some scuffed from being manhandled by the police, rather than its meticulous reconstruction.

Facebook Twitter Pinterest Manhandled … Brian Haw’s Parliamnet Square protest camp in 2002. Photograph: Andy Butterton/PA

Wallinger has been seen as engaging in an act of visual protest, and certainly at the time the Tate investment of £90,000 in the work was seen as an institutional stand against the Labour government. But the ideas explored in this piece were clearly about the nature of reproduction, and the shift from spontaneous protest to considered art. These are not ideas that in themselves can have anything like the impact – they lack the force of Haw’s brave, exhausted vigil.

Haw died in office. He abandoned his megaphone and his placards in 2011 to be operated on for the lung cancer that swiftly killed him. Did his dogged, sacrificial fight change anything? Do any protests have an effect? They create a sense of solidarity: if anything good has come out of the current political situations in Britain and the US, it is that small differences can be more easily forgotten as you march against the big problems. The pleasure in this can provide a necessary source of strength to people who might go on to participate in more targeted forms of activism.

Looking back on the Aldermaston march, the science fiction writer John Brunner, who wrote the lyrics to “The H-Bomb’s Thunder”, described it as “by far the most exciting and moving experience I can remember”. Arguably, the presence of resistance is enough, an art in itself, if we accept Kennard’s view, and a source of comfort to those involved. Certainly, watching that footage, looking at those banners, I find that it’s possible to move beyond nostalgia to relive the optimism of 1958. And it’s a message that can inspire us even now. “Men and women stand together. / Do not heed the men of war. / Make your minds up now or never, / Ban the bomb for evermore.”