During his five years as director of the Victoria and Albert Museum, Martin Roth put the London institution on the international stage, travelling tirelessly as its “ambassador”. His resignation last September – greeted with widespread surprise – was prompted to a significant extent by his disappointment at Britain’s referendum decision the previous June to leave the EU.

Full of his usual energy, he left London with ambitious plans to become more involved in global issues. However, only a few weeks later he was diagnosed with cancer, from which he has died, aged 62.

Well known on the museum scene in his native Germany, Roth had a low profile in Britain, and his appointment to the V&A had also been greeted with surprise. His personality and approach to leadership turned out to be very different from that of his predecessor, the more scholarly Sir Mark Jones.

Always impeccably dressed, Roth enjoyed mixing with figures of international standing to advance the causes of cultural exchange and what he declared to be “the world’s leading museum of art and design”. Confident and forthright, he enjoyed controversy and debate.

Under his stewardship the V&A prospered, with visitor numbers rising to 3.5m, and in 2016 it won the Art Fund museum of the year award. There was a string of highly popular exhibitions, including David Bowie Is (also seen in 10 other countries); Alexander McQueen: Savage Beauty; and Disobedient Objects, on design and social change.

Starman costume from Top of the Pops in 1972 at the David Bowie Is exhibition at the V&A in 2013. Photograph: Leon Neal/Getty Images

Roth oversaw building work on a £50m extension on Exhibition Road with a new entrance and underground temporary exhibition gallery, which opened to applause in June. V&A-branded galleries are also nearing completion in Shenzhen (in China, on the border with Hong Kong, opening in December) and Dundee (due for 2018). Roth’s most ambitious legacy may well be a branch of the V&A in east London, a massive new gallery building planned for the former Olympic site and set to open in 2021.

On his arrival at the V&A, Roth instituted management changes to make the museum more efficient. This initially created difficulties with both trustees and staff. Feelings among curators remained mixed during his tenure, unsurprisingly in a museum with wide collecting fields. Some curators outside the performance and fashion collections felt that the V&A’s traditional focus on the decorative and fine arts was being sidelined in favour of blockbuster shows.

When Roth was away he left much of the administration to his deputy, Tim Reeve, who recalled working with him as being “scary, fun, exhilarating... encouraging us all to take risks, to search for the new, the different, the alternative”. Reeve came to think of him as a friend, “sometimes infuriating, but mostly inspiring”.

When Roth decided to leave, he made a clean break with the museum. As he told me in an interview: “It’s like a love affair. Once you split, you don’t want to share the kitchen table.” A month after the announcement, he moved to Berlin, where he had been offered the post of president of Germany’s Institute for Foreign Relations, which deals with cultural exchanges. Though his health was deteriorating, Roth took up the post at the start of July.

He was born in Stuttgart: his mother was a tailor and his father an electrician. For his doctorate at the Eberhard Karls University in Tübingen (1987), he wrote a thesis on museums and cultural politics in Germany from 1871 to the end of the Third Reich. Then he did research at the Maison des Sciences de l’Homme in Paris and the Getty Research Institute in Los Angeles. After serving from 1989 as a curator at the German Historical Museum in Berlin, he moved to Dresden in 1991, just after the country was reunified, to become director of the German Hygiene Museum, an important medical museum with popular appeal. From 1996 he helped develop the 2000 Hanover Expo, and he served as president of the German Museums Association (1995-2003).

Roth’s big break came in 2001, when he was appointed director general of the Dresden State Art Collections, which comprises 12 museums. The city had suffered terribly from Allied bombing during the second world war, so this was an another ever-present reminder of the effects of conflict. One year later he faced the challenge of dealing with a catastrophic flood of the River Elbe and its tributaries. After the initial rescue operation of the Dresden artworks, he oversaw the construction of a safe storage facility as part of the renovated Albertinum gallery.

The Alexander McQueen: Savage Beauty exhibition at the V&A in 2015. Photograph: Anthony Harvey/Getty Images

When Roth left Dresden, it was to go to the V&A. He told me that moving on from the latter came partly because of the referendum result. That was “just an element, but definitely an element”. Roth was characteristically outspoken in his comments: “Brexit was about telling people lies, Little England coming back, new nationalism returning to Europe, xenophobia, hate crimes.” Brexit strengthened his determination to return to Berlin and become more politically engaged. Roth was very disturbed by the recent rise of nationalism and racial tensions throughout Europe, and he saw cultural ties as way of bringing peoples together and fighting hatred. He was determined to use his new post at the Institute for Foreign Relations to make the organisation more of “an art and culture mediator”.

In May, however, Roth became embroiled in controversy when he co-curated the Azerbaijan pavilion at the Venice Biennale, with critics pointing to its government’s poor human rights record. Although admitting to some regrets over his involvement, Roth maintained that “the art world also needs to talk to regimes it opposes”.

He is survived by his wife Harriet (nee Hauger), a son and two daughters.

Martin Bailey

Hella Pick writes: Martin Roth was a citizen of the world, a convinced European and a German who felt deeply about the need to redeem the Holocaust. He was an imaginative and enterprising practitioner of cultural diplomacy who passionately believed that the great public museums not only have an educational role but can help to build bridges across political divides.

Both as director of the Dresden State galleries and more recently at the V&A, Martin reached out to the wider world. While at Dresden he developed close links with the Pushkin State Museum of Fine Arts in Moscow and its director, Irina Antonova. His diplomatic skills led among much else to an exhibition in the National Museum of China, in Beijing, dedicated to the Enlightenment – an extraordinary achievement which nevertheless caused considerable controversy in Germany. Roth’s critics argued that he had betrayed the cause of human rights.

I first met Martin when he participated in an arts conference organised by Lord Weidenfeld’s Institute for Strategic Dialogue, where he delivered a paper that argued for closer cooperation between national museums. This led both to collaboration over a number of arts-related conferences in Dresden and once in New York, and above all to a close friendship.

His achievements in restoring Dresden’s collections to their full glory reached their peak with the reopening of the Grünes Gewölbe (Green Vault), Europe’s greatest collection of treasures. But he was equally proud when the restored Türckische Kammer (Turkish Chamber) was reopened, accompanied by a conference on the Ottoman influence on Germany and how it related to the country’s large present-day Turkish community.

Martin was immensely proud when he was invited to take charge of the V&A, though I remember that one of his first concerns was whether British Jews would find it difficult to see a German at the helm of such a national institution. He had many plans for his post-V&A life, not least that he would be able to spend more time with Harriet, who fully supported his work even though it meant that he was so often away. He had hoped to play an active role in the strengthening of the European project while maintaining his links with the museum world. When the Roths left London last year they were convinced of a new lease of fulfilling life. It was sadly not to be.

• Martin Roth, museum director, born 16 January 1955; died 6 August 2017