The director of the Victoria and Albert Museum, Tristram Hunt, has mounted a strong defence of the museum’s relationship with the Sacklers, the family accused of making a profit from the US opioid crisis.

Hunt said the London museum was proud to have received support from the family over a number of years. “We are not going to be taking names down or denying the past,” he said.

The Mortimer and Raymond branches of the Sackler family, prolific philanthropists to arts organisations in the US and UK, own Purdue Pharma, the maker of the opioid painkiller OxyContin. Eight family members are named in a US lawsuit accusing them of helping to create “the worst drug crisis in American history”.

One of those is Dame Theresa Sackler, one of the most generous arts patrons in the UK and a trustee of the V&A. The Sackler name adorns the £2m courtyard of the gallery’s Exhibition Road entrance, which opened in 2017.

The Sackler family has said it will not give any more money, a decision Hunt said he respected. “We have had strong support from the Sackler family: Theresa Sackler is a trustee of the museum. I think they are reflecting on the controversy; they dispute some elements of it. They have made the decision not to give any more funds.”

Sackler courtyard at the V&A in London. Photograph: Anthony Weller/View/Rex/Shutterstock

The former Labour MP said big government cuts to arts funding meant museums and galleries had to seek out a broad range of backers but it was a “tough environment”. Addressing journalists at the launch of its annual review, he said: “You do your job, which is absolutely right, in criticising anyone who gives money to cultural institutions whilst wanting support for exhibitions.”

An estimated £80m of Sackler money has been given to the arts in the UK, as well as science, health and education, and the family name appears on dozens of cultural buildings including the Sackler escalators at Tate Modern, and the Sackler Room at the National Gallery, containing John Constable’s The Hay Wain and George Stubbs’s Whistlejacket.

Hunt said Theresa Sackler’s tenure as a trustee was due to come to an end in the early autumn and he strongly defended her as a fit person to have served in the role. He told the BBC: “Theresa brings a lot to the conversation in terms of her background as a primary school teacher and her focus on education. We’re proud to have been supported by the Sacklers.”

In March Theresa Sackler announced that the Sackler Trust and the Dr Mortimer and Theresa Sackler Foundation were suspending all new charitable giving in the UK, saying there was a danger of it being a “distraction” for the bodies the foundation supported.

In a statement on behalf of the Sackler Trust trustees, she said: “I am deeply saddened by the addiction crisis in America and support the actions Purdue Pharma is taking to help tackle the situation, whilst still rejecting the false allegations made against the company and several members of the Sackler family.”

Purdue is facing lawsuits from nearly every US state over the role of OxyContin in the deadly opioid crisis.

In 2007, the company was fined for marketing OxyContin “with intent to defraud or mislead” regulators.

Drug overdoses kill more than 72,000 people in the US each year. About 49,000 deaths are caused by opioids, including heroin and prescription painkillers such as fentanyl.

In recent months, the US photographer Nan Goldin has been on the frontline of protests to campaign against links between art institutions and the Sacklers. Goldin became addicted to OxyContin after being prescribed it for tendinitis in 2014.

Purdue Pharma denies any wrongdoing, as do the Sackler family members named in recent cases.

The controversy was aired as the museum looked forward to 2020, announcing an exhibition programme that will include shows exploring the kimono, Renaissance watercolours, Alice in Wonderland, and the cultural history of Iran.

The Iran exhibition, due to open in October, comes as tensions continue to mount between Tehran and Washington. Last month Donald Trump imposed new sanctions on Iran.

Hunt said curators had been involved in close discussions with the Iranian embassy in London and was working with the National Museum of Iran on loans. “It’s not easy, not in terms of cultural relations … but the landscape is not easy. Every week it becomes more challenging but in a sense that means every week it is more important to do.”

He said it became more valuable as an exhibition as the militaristic language was ramped up.

Less tricky will be a show opening in April which promises to be the biggest exhibition ever devoted to bags. It will include more than 300 objects from the 16th century to the present day, including tiny finger purses, travelling trunks, rucksacks, Birkin bags and Louis Vuitton luggage. One of Margaret Thatcher’s handbags is expected as a loan.

“It’s very V&A,” said Hunt, a leather briefcase carrier. “It’s material culture, it’s international, east and west, it’s craft, it’s beauty but also there is a very interesting social history there as well.”