Hundreds of figures in the arts and science, including Oscar-winning actor Mark Rylance, artist Conrad Atkinson, composer Matthew Herbert and author Naomi Klein, have called for BP’s new five-year sponsorship deals with some of Britain’s leading cultural institutions to be cancelled.

Rylance, who is the former artistic director of Shakespeare’s Globe theatre and star of Steven Spielberg’s new film The BFG, heads a list of 214 signatories to a letter in the Times claiming that BP uses art sponsorship to help develop its interests in oil extraction, which must be reduced to avoid rapid climate change.

It comes after BP announced it would invest £7.5m in the British Museum, National Portrait Gallery, Royal Opera House and Royal Shakespeare Company last week. Other signatories include actor Ezra Miller, Nigerian poet Nnimmo Bassey, environmentalist Jonathon Porritt, and climate science historian Naomi Oreskes, who have called the deals “outdated and unacceptable”.

The letter, organised by Art Not Oil, a coalition of campaign groups, continues: “We cannot afford another five years of BP-branded culture. We believe museums, theatres and galleries are public institutions that must play a positive role in taking urgent climate action and defending human rights.

“If the world is to avoid rapid and devastating climate change in the coming decades, most of the oil on BP’s books cannot be burned. Meanwhile, the company continues acting in defiance of the Paris agreement on climate change, and harming lives every day - despite community resistance from the Gulf Coast to West Papua to Australia.”

The letter adds that it has become cheaper for BP to get its brand on major museums and theatres (£375,000 a year for each institution, on average) than the cost of a short billboard campaign. “Surveys show that a majority of Londoners, and the British Museum’s own staff, are against BP sponsorship,” it says.

Anna Galkina, from Art Not Oil, said in a statement: “Oil sponsorship is meant to buy artists’ silence and audiences’ approval, and silence the people who live on the frontlines of oil extraction and climate change.”

Earlier this year, BP ended its 26-year sponsorship of Tate and 34-year sponsorship of Edinburgh International Festival, blaming the “extremely challenging business environment” rather than years of protest against the deals - including demonstrators spending 25 hours scrawling climate change messages in charcoal on the floor of Tate Modern’s Turbine Hall.

The British Museum, National Portrait Gallery, Royal Opera House and Royal Shakespeare Company (RSC) have also seen creative protest performances criticising their relationship with BP. Theatrical protest group BP or not BP? invaded the RSC’s stages repeatedly in 2012 when BP sponsored a series of plays there, and have performed without permission in the British Museum 18 times. Art collective Liberate Tate also performed at several of the institutions.

A previous open letter to Dr Hartwig Fischer, the new director of the British Museum in April, signed by Rylance, Emma Thompson, Mark Ruffalo and shadow chancellor, John McDonnell, called on him to drop BP as a sponsor.

Catherine Mallyon, executive director of RSC, said: “The contribution of BP means that we can offer £5 tickets to 16 to 25-year-olds, allowing many young people the chance to see our work all over the country. We know that people value this opportunity as they can come to see our work on a regular basis. It also helps us to introduce a new audience to Shakespeare and live theatre.

“As a charity we receive income from many important sources, which includes the business sector. It is one of the ways the RSC is funded, alongside ticket sales, public investment, private philanthropy and commercial activity. In a challenging funding environment we look continuously to maintain existing support and secure new partners, and every one of our relationships helps us to deliver our work, on and off the stage, to the widest possible audience.”

A spokesperson for the British Museum said that BP sponsorship had enabled the museum to host a series of exhibitions and events. “From understanding the Emperor Hadrian and the legend of the Vikings, to the significance of Indigenous Australia and the Mexican Day of the Dead, these exhibitions and events have been enjoyed by millions of visitors to the museum and have deepened understanding of the world’s many cultures and their interconnectedness. The museum is grateful to BP who have confirmed they will continue to support the British Museum exhibition programme for a further five years.”

Alex Beard, chief executive of the Royal Opera House, said: “One of the benefits of such long‐term support [from BP] is that you can really build and develop a partnership, and to have the BP Big Screen programme consistently providing opportunities for people up and down the country to access world‐class ballet and opera for free is fantastic.”

BP declined to comment directly on the letter but pointed out that in total more than 50 million people have engaged with BP supported arts and cultural activities since 1990. When announcing £7.5m deal last week, Peter Mather the BP Group regional vice-president, Europe said: “Our continued support will enable these institutions to forward plan engaging, educational and powerful exhibitions and performances that will be enjoyed by millions here in the UK and beyond.”