Five winners of the Turner prize are demanding an end to BP’s sponsorship of the National Portrait Gallery, stepping up the campaign against big oil’s involvement in the arts.

Antony Gormley, Rachel Whiteread, Anish Kapoor, Gillian Wearing and Mark Wallinger are among a group of almost 80 leading artists, including winners of the BP portrait award, who have written to the gallery’s director, Nicholas Cullinan, highlighting the company’s role as one of the world’s biggest fossil fuel producers and calling on him to cut ties. The group say it is necessary to ensure the gallery remains a “forward-looking institution that’s on the right side of history”.

The move by some of the UK’s best known cultural figures represents a dramatic escalation in the campaign. Last month Mark Rylance resigned from the Royal Shakespeare Company over its sponsorship deal with BP, telling the Guardian it allowed the company to “obscure the destructive reality of its activities”.

Rylance said he did not wish to be associated with BP any more than with “an arms dealer or a tobacco salesman”.

Gormley told the Guardian he felt he had no choice but to make a stand. “All artists – from the cave dwellers of Lascaux to the most oblique minimalists – have made work in anticipation that those sculptures, paintings, installations and experiences will speak to their descendants,” he said.

“Art has always been a practice of hope. BP have demonstrated that they have no interest in our collective future and will jeopardise it in the pursuit of profit. Science tells us that BP’s business threatens our very way of life. We have no choice but to respond.”

BP has sponsored the gallery’s portrait award for 30 years, with the current five-year arrangement announced in 2016 as part of a £7.5m deal with four leading UK institutions: the Royal Opera House, British Museum, National Portrait Gallery and Royal Shakespeare Company.

The campaign against fossil fuel corporations’ sponsorship of the arts has escalated in recent months amid growing concern about the scale and severity of the climate crisis.

In February hundreds of people occupied the British Museum and last month a judge and several leading artists wrote to Cullinan on the eve of the National Portrait Gallery’s annual awards calling on it to end its links to the company. A subsequent demonstration disrupted the awards ceremony.

This week Extinction Rebellion protesters staged a “die-in” protest outside the Royal Opera House over its BP sponsorship.

Jess Worth, from the campaign group Culture Unstained, said: “As the news on climate change gets more and more dire, the way that artists are now stepping up is a real source of hope. They are part of a much wider movement that is starting to genuinely disrupt business as usual for the oil industry and make the prospect of a safer, healthier zero-carbon world seem much more possible.”

Campaigners say the pressure they are putting on is starting to make an impact. This week the London Stock Exchange reclassified fossil fuel corporations as non-renewable energy companies to distinguish between heavily polluting companies and greener producers.

A few days later the head of strategy at BP admitted some of its oil and gas reserves “won’t see the light of day”, in part because of investors’ pressure to stick to lower-carbon projects.

The secretary general of the oil producers’ group Opec has complained that the “growing mass mobilisation of world opinion … against oil” was “perhaps the greatest threat to our industry” and was “beginning to … dictate policies and corporate decisions, including investment in the industry”.

In their letter, the artists point to BP’s role in furthering the climate crisis and their “collective responsibility to act”. It concludes: “The loss of BP as a source of funding is a cost worth bearing, until the company changes course.” It also demands the gallery immediately remove BP from the judging panel for the annual portrait award.

In response, Cullinan acknowledged the letter raised “important questions about the environment and funding for the arts” that were “of concern to us all.”

But he said that with government funding accounting for just 33% of its income, the gallery had to work with a wide range of corporate partners.

“BP’s long-term support for the portrait award directly encourages the work of talented artists across the world,” he said. “It also enables free admission to the exhibition, which attracted over 275,000 visitors in London last year. For this we are grateful.”

Cullinan said the gallery was continually aiming to expand its list of corporate supporters although attracting new sponsorship was “challenging in the current economic conditions”.

“Our commitment is to act in good faith and for the public good,” he said. “Our challenge is to fulfil our remit, fund our work for the public and find positive solutions appropriate to the changing times in which we live.”

A spokesperson for BP said it was proud of its history of arts sponsorship, which had allowed millions of people to visit exhibitions and events.

They added: “We recognise the world is on an unsustainable path, more needs to be done to fix that and the world needs to move to net zero carbon emissions in the decades to come … the answer will come through coming together, building understanding and collaborating to find real solutions rather than through further polarisation and exacerbating divisions.”