In April 2012, just six months after Colonel Gaddafi had been killed by rebel forces in Sirte, Libya, and as fighting between rival militias continued, an exhibition of British street art opened at the Dar Al-Fagi Hassan Art Gallery in Tripoli and then in Benghazi. The works of Banksy and D*Face were shown alongside photographs of graffiti by Libyan artists who had scrawled their messages of dissent furtively on city streets as the uprising against Gaddafi’s regime gathered pace. The show, organised by the Victoria and Albert Museum in London with the support of the British Council, was intended as an act of solidarity with the Libyan people. “I thought it was so important to be there immediately, not to wait. I wanted to say to the Libyans, ‘We are here; you can count on us,’ ” explains the director of the V&A, Martin Roth.

It was an extraordinary gesture from a museum of decorative arts. Not long ago, our top national art collections were focused primarily on the custodianship of objects in their care, on scholarship and on exhibitions. Today, our museums are also politically engaged, globally connected and incredibly skilled in the arts of international cultural diplomacy, their reach sometimes extending beyond that of governments.

One institution in particular lies at the heart of this story: the British Museum. Forged in the Enlightenment, expanded through empire, it is now one of the great repositories of world culture. Under the leadership of Neil MacGregor, who took the helm in August 2002, it has carved out a significant role for itself as a global organisation with global responsibilities. The policy shift became apparent following the sacking of the National Museum of Iraq. On 12 April 2003, news began to emerge of the systematic looting of the museum, which had been left unprotected as US forces began to take control of Baghdad. Hundreds of people rushed through the galleries smashing glass cabinets to grab objects and attacking sculptures with iron bars before moving on to the building’s vaults. Priceless, irreplaceable works of art disappeared. Statues too heavy to move were decapitated. The destruction was terrible. Three days later, MacGregor held a press conference at the British Museum in London with the UK’s then minister of culture, Tessa Jowell. He announced that his institution would take a lead in providing assistance to curators in Iraq and would act as a co-ordinator for other museums that wanted to help. Soon after that, he despatched a team of three curators and six conservators to assist museum staff in Baghdad.

The initiative followed a plea for help from curators at the ransacked museum who had long-standing connections with counterparts in London. “When they came under attack, they quite naturally phoned us and asked us, ‘Can you do something?’ ” MacGregor says. “To be part of a global community of people who look after the things from the past is not just about writing articles for learned journals, publishing catalogues and sharing knowledge. It is about helping each other now.”

Roth shares this view. When we meet, he is just back from a visit to Syrian refugee camps in Lebanon, to which he travelled with the German foreign minister, Frank-Walter Steinmeier. Concerned at reports that Isis was looting and trafficking antiquities to help fund its activities, Roth spent his time in the camps briefing relief organisations and NGOs on the importance of Syria’s cultural heritage and its history. Accounts have emerged that the terrorist organisation is sacking museum collections and seizing objects from ethnic and religious minorities. It is also allowing local people to dig at archaeological sites in exchange for a percentage of the value of any finds, according to a report in the New York Times. “My main purpose is to help to stop, or at least to make more difficult, the way Isis takes objects out of the country and sells them here on the art market,” says Roth, hinting at plans to set up a joint force of museums to combat this trade.

Such campaigns, designed to safeguard the cultural heritage of countries at war, are often low on the list of government priorities. So, institutions such as the British Museum and the V&A are in effect stepping in to fill a gap in the political thinking, a failure to grasp that, when the fighting is over, no matter how long it lasts, culture will matter more than ever as nations struggle to reknit the civic fabric of their lives.

But the influence of our museums is even greater when dealing with countries at peace, building relationships with colleagues around the world, irrespective of political regimes. Take Iran. In 2005, relations between the Middle Eastern state and the west were at a low point after the inauguration in August of the hardline conservative Mahmoud Ahmadinejad as president and with concerns growing about Iran’s nuclear programme. A month later, the British Museum launched a stunning exhibition on the ancient Persian empire and its great kings, arguing that the Persians’ achievements had been overlooked in favour of the Greeks and the Romans. This was an exhibition “calculated to turn history on its head”, in the words of the Guardian’s Jonathan Jones. It was also a diplomatic coup; many of the objects on display came from the National Museum in Tehran and their loan had to be renegotiated at the last minute following Ahmadinejad’s election. While denouncing the west and calling for the destruction of Israel, Ahmadinejad still allowed multiple masterpieces to leave the country for display in Britain. Why?

Despite the rhetoric, there are few regimes that wish to sever all ties with the international community. Cultural exchanges are seen as a neutral way of maintaining contact, particularly when they involve ancient objects that recall a glorious past. In short, antiquities are usually a safe zone. Four years after its Persian empire exhibition, the British Museum mounted another major show with loans from Iran, this one devoted to Shah ‘Abbas, the 16th- and 17th-century ruler who consolidated the pre-eminence of Shia Islam in his territories. The value of these displays, MacGregor says, is that they increased our understanding of how Iran views itself, its history and its role as a Shia country in the Middle East today, helping us to “see the world through Iranian eyes”.

In 2010, the British Museum returned the favour by sending one of its greatest anti­quities, the Cyrus Cylinder, to Iran. The clay drum was made around 539BC after the Persian king Cyrus had conquered Babylon. It records this victory in dense cuneiform script and describes how the peoples enslaved by the previous rulers of the city state were then allowed to return home. It also proclaims the rights of worshippers to honour their own gods. During its seven-month stopover in Tehran, the antiquity was seen by more than a million Iranians. The loan showed that “in spite of the . . . glacial state of diplomatic relations, British and Iranian colleagues can, in some areas, work happily together. And it raises the question of whether more areas of collaboration might be developed,” wrote MacGregor in a newspaper article at the time. The display of the antiquity in Iran also “provoked lively debate about what it means today to be Iranian . . . Is the Cylinder evidence of a long, robust, and specifically Iranian tradition, a national identity far older than Islamic Iran, founded on ideals of justice, tolerance and peace? President Ahmadinejad, in his speech at the opening ceremony, suggested just this – that in the words of the Cyrus Cylinder, there is something of the Iranian soul.”

It is impossible to quantify the efficacy of such cultural initiatives in improving relations between countries. “It’s very difficult to draw a clear, evidential link between a particular piece of activity and an outcome, but conventional diplomacy suffers from this, too. It is about establishing long-term relationships,” says Sir Martin Davidson, chief executive of the British Council, which is active in more than 100 countries and is part funded by the Foreign Office.

It is precisely when nations are struggling to find common ground that these projects matter most, says Davidson, who adds that if relations between Britain and Russia continue to deteriorate, he will seek to increase the British Council’s presence and activities in that country.

That our museums are free to engage with nations that our governments shun is testament to the foresight of their founders, who wanted them to be independent of parliament and decreed that they should be overseen by boards of trustees. This is not the case in continental Europe, where most museums are controlled by ministries of culture and it is more difficult for them to operate in defiance of government policy. In the United States, museums rely predominantly on private funding and, mindful of their patrons’ sensitivities, are much more cautious in engaging with the outside world. So British museums occupy a unique place in the cultural sphere, their ability to think and act as autonomous entities being enshrined in their very DNA.

This freedom has enabled our museums to disseminate their collections widely. The likes of MacGregor argue that the objects in his institution are part of the world’s heritage, not just our own, and should therefore be shared as widely as possible. Not everyone accepts this narrative. Some of the greatest treasures in British collections were looted from their country of origin in the colonial era, sometimes brutally, or were acquired in dubious circumstances, and should be returned, they argue, because cultural objects belong primarily to the people who made them and the places they were made for. Chief among the claimants are the Greeks, who have spent decades campaigning for the British Museum to return the Parthenon sculptures bought by Lord Elgin from the Ottomans in the early 19th century. They even built a new museum to house them. But the British Museum has refused to budge on the matter, repeatedly stating that it is prevented by law from de-accessioning objects.

Other contested items are sculptures from the kingdom of Benin, in present-day Nigeria, seized during a punitive British expedition in 1897, and indigenous Australian artefacts. To return objects would set a dangerous precedent, the museum believes. It could, if taken to its natural conclusion, lead to the unravelling of the entire collection, one of the great ironies of the British Museum being that there is precious little British material housed inside it. To allay these calls for restitution, MacGregor has championed the Enlightenment concept of the encyclopaedic collection, arguing that it is the reach and scope of the cultures it encompasses that gives the museum its power.

Successive governments have recognised this power: in 2008 MacGregor was appointed chairman of the World Collections Programme, a new diplomatic role intended to promote six UK institutions, including the British Museum, the V&A and Tate, internationally. “Art can often reach places that diplomacy cannot,” said the Labour culture secretary of the time, James Purnell, announcing the post. Four years later when funding for the programme was cut, the new culture secretary, Jeremy Hunt, told museums that he hoped their international work would continue and that they should focus on “China, India, Brazil, the Gulf states, Russia and Japan”, nations that the coalition government would prioritise, he said. Last month the government announced funding of £300,000, administered by the British Museum, to enable a series of exchanges between museums in the UK and China.

When the interests of governments and cultural organisations align in this way, the result is an explosion of artistic exchanges. Nowhere is this more apparent than in our current relations with China. As Britain has pushed for greater trade with the country, our museums have embarked on numerous projects with Chinese colleagues and hosted a string of exhibitions drawn from the country’s rich collections. The latest is a spectacular exploration of 50 years of the Ming Dynasty on display at the British Museum. The show focuses on the years between 1400 and 1450, when the emperor established a network of princely fiefdoms across his vast territories, presided over by 24 of his sons; the capital moved from Nanjing to Beijing in that period, and the explorer Zheng He commanded great armadas that sailed to south-east Asia, the Middle East and Africa. About one-third of the 280 objects on view have come from the collections of 30 Chinese museums, their loan facilitated by Art Exhibitions China (AEC), an organisation set up in 1971 to oversee the export of China’s cultural heritage.

In the past four decades AEC has sent 200 exhibitions to 30 countries, with the focus always on China’s historic dynasties and never on contemporary artists, whose work is too often critical of those in power. In return, China has welcomed several shows of objects from the collections of European museums – and sometimes the results are incongruous. In 2011, the National Museum of China hosted a huge exhibition on the European Enlightenment with all the displays on loan from Germany. Just two days after the opening, as the press was still marvelling at the spectacle of a show devoted to science, reason and law in a museum on Tiananmen Square, the state authorities arrested the dissident artist Ai Weiwei in a crackdown on critics, writers, lawyers and artists. The German press was horrified. Some called for the immediate return of all the displays to Germany. “They crucified me,” recalls Roth, who was then serving as director of the Dresden State Art Collections. “They accused me of bending down in front of a dictatorial regime . . . their expectations were unrealistic; they thought we’d do an exhibition on the Enlightenment in Tiananmen Square and that a revolution would start in China the next day.”

Yet he has no regrets. To engage with countries is always better than to boycott them, Roth says: it is the only way to effect change over time. At the V&A, he has continued to build alliances in China, entering into a partnership with the conglomerate China Merchants Group to create a design museum in Shenzhen, due to open in 2016; it will host displays from the London museum and be overseen by a V&A curator.

Directors such as Roth and MacGregor have shown that culture can be a bridge between nations that are barely talking to one another. And they have proved that, by bringing people together, objects can succeed where politicians fail. Whether they have brought about a shift in institutional thinking remains to be seen. For now, however, the global influence of our museums has never been greater.

Cristina Ruiz is the editor at large of the Art Newspaper

“Ming: 50 Years That Changed China” runs until 5 January 2015 at the British Museum, London WC1. Details: britishmuseum.org