Bomb Culture was the name of poet and painter Jeff Nuttall's personal analysis of the 1960s counter-culture from a frontline which, in 1968, when his book was published, was still very much in place. Its title referred to how the threat of nuclear war had influenced a post-Hiroshima generation who embraced anti-nuclear sentiments through the Campaign For Nuclear Disarmament (CND), founded in 1957 with a unilateral opposition to what would now be termed Weapons of Mass Destruction.

Much of that spirit of dissent can be found in Here Comes Everybody and Pop and Boom: 70 Years of Nuclear Culture, two exhibitions which combine activism and art in a way where protest and people power becomes both mass spectacle and a work of art in itself. Where Here Comes Everybody shows off a series of photomontages and digital prints by kennardphillipps, the collaborative duo of Peter Kennard and Cat Phillipps, Pop and Boom is a compendium of pop cultural artefacts inspired by the nuclear threat, and pulled together by Greenham Common veteran Carol Naughton to commemorate the 70th anniversary of the Hiroshima bombing.

'If you just show images of the disaster itself,' Naughton explains, 'there's a horror to it and people switch off, so I wanted to commemorate it in a way that felt real for people, and show how nuclear weapons have influenced popular culture. In the first years it was purely reactive, then in the eighties the whole thing took off as protest rose, and the two together were very powerful. Nowadays nuclear weapons in books and films are incidental, and people don't realise what nuclear weapons are, so part of the exhibition is to remind people of their significance.'

It was Kennard's images in the 1980s for CND, Stop the War and other campaign groups that provided a visual identity for a youth-driven protest movement that was immediate and subversive in a way that chimed with the post-punk era's alternative DIY cut-and-paste aesthetic.

'At that time it seemed like EP Thompson, the veteran CND activist, would be in the NME every week,' Kennard observes. 'It was cruise missiles that brought people together, but today they're seen as acceptable and as a part of life. Part of our exhibition is to show people what's been going on, so you get an aesthetic experience, but it also might activate them, even if that might take 15 years.'

This trickle-down effect can be seen in the way the Greenham protests against Trident, which Kennard likens to 'a living collage’, influenced the Occupy movement's collective actions that re-engaged people with grassroots protest following the politically moribund New Labour years. kennardphillips is a direct result of this, with their best-known work probably being Photo Op, which fuses together an image of a grinning Tony Blair taking a selfie on his mobile phone against a backdrop of a burning oilfield in Iraq.

Described by the Guardian as 'the definitive work of art about the Iraq war', kennardphillipps' 2005 piece was chosen by the Imperial War Museum North in Manchester as the image for a poster to promote an exhibition about the relationship between contemporary art and war. With two of the UK's biggest advertising companies refusing to display it, this exposed how public spaces can be controlled by commercial forces.

Phillips agrees with Kennard that their fusion of activism and art aims to 'activate a conversation. The space in Stills The space in Stills for Here Comes Everybody is very much a space for conversation, and that's going to develop into a conversation with the stuff that's already there at the moment as well as the stuff that's going to come in, but there's a verbal conversation as well, and the space has been designed as a place to hang out as much as anything. There's no one thing that dominates the space, and it's going to be completely different in a couple of weeks.'

This will be the result of whatever comes from kennardphillipps' War on War Room, an open access workshop space that will set up shop in the St James Centre, where, assisted by kennardphillipps with Glasgow artist Scott Laing, people will be able to make their own work which will then form part of Here Comes Everybody.

'I think that's where I see what art can do,' says Naughton. 'It's about inspiring people to take an issue and come to the shopping centre and express how you feel about it. It's not just showing the history of something. It's showing how public protest can change things.'

kennardphillipps, Here Comes Everybody, Stills, 622 6200, until 25 Oct, free; The War on War Room, St James Centre, until 31 Aug, free.
Pop and Boom, Gayfield Creative Spaces, gayfield.co.uk, until 20 Aug, free. The exhibition will open with Launching The Bomb on 6 Aug, featuring performances by Mark Thomas, Vladimir McTavish and Samba Sene and Divan, plus appearances by Peter Kennard and Cat Phillipps.