When Extinction Rebellion activists shut down London in April, we sounded the alarm loud and clear about the climate and ecological crisis that threatens humanity’s very survival. In response, around the world, governments, local councils, companies and professionals are stepping up and declaring a climate emergency.

And yet, the silence from the major agents of climate destruction remains deafening. In the heart of London, the city that heard our rallying cry to “Act as if the truth is real”, BP, a global fossil fuel giant, is sponsoring the Royal Opera House Big Screen in Trafalgar Square. Rather than denouncing the damage these companies continue to do to our planet, our cultural institutions are lending them legitimacy.

On Tuesday evening, Extinction Rebellion Lambeth and rebels from across London will protest before the Big Screen showing of Romeo and Juliet. Their own silent tragedy of Petroleo and Fueliet will highlight the pain and devastation caused to the silent masses and demand our leaders end complicity in climate breakdown.

Sponsorship deals allow BP to promote itself as a philanthropic organisation and a responsible player in society

Oil majors have known what is at stake for a long time and have waged multimillion-dollar lobbying campaigns, spinning a web of deceit. Now is the time to expose how they use sponsorship of arts and cultural organisations to greenwash the truth about what they do. BP has made the third biggest contribution to climate change of any company in history. It is time to say: no more.

Fossil fuels are the main drivers of the climate crisis, and as coal faces an investor exodus, new oil and gas infrastructure is a growing global threat. In the UK, we’ve seen electricity generation become coal-free for more than a fortnight. This is great news; now the fight for clean energy in the UK must aim at stopping oil and gas expansion, and boosting solar, wind power, battery storage and other low-carbon technology. Further gas or oil exploration is incompatible with keeping global warming below the 1.5 degrees we need to mitigate the risk of societal collapse, mass migration and hunger. New oil exploration is utterly incompatible with preserving life on Earth. Nonetheless, BP plans to spend over $70bn in new gas and oil fields in the coming decade.

A Greenpeace Unearthed investigation recently exposed how BP lobbied the Donald Trump administration for drilling rights in the protected Arctic national wildlife refuge, one of the last untouched ecosystems on Earth. This is despite the fact that the company is already responsible for 200,000 gallons of crude oil spilled from pipelines in Alaska in 2006 and the Deepwater Horizon tragedy in 2010.

Governments and investors are belatedly waking up to high risk of oil and gas. Last year, New York City divested US$5bn. On Wednesday, the trillion-dollar Norwegian sovereign wealth fund will divest up to US$8bn from around 150 oil and gas exploration companies. BP and the oil majors might not be part of that exclusion list, yet, but the tide is turning.

To act in accordance with the realities of climate breakdown, to stand in solidarity with the millions of people already feeling its catastrophic effects, to have any hope of turning the ship around in the small window of time we have left, we can no longer sanction the behaviour of the oil majors. By allowing them to share a platform with our respected cultural organisations we are complicit in the destruction they are wreaking on our planet.

Sponsorship deals allow BP to promote itself as a philanthropic organisation and a responsible player in society, maintaining its social licence to operate, while deflecting attention from its destructive impacts on communities and national economies.

In April, Extinction Rebellion targeted Shell’s London headquarters. Now it is the turn of BP. In what looks set to be the largest protest against oil sponsorship to date, Extinction Rebellion Lambeth is joining the art-not-oil movement in calling for our cultural institutions to sever their ties with big oil. In February, hundreds of activists occupied the British Museum to protest against its relationship with the oil giant, and today one of the judges of the prestigious Portrait Awards has spoken out and demanded the National Portrait Gallery remove BP sponsorship.

The environmental movement is coming together and the pressure is relentless; society will no longer normalise the actions of the oil majors. BP used to be a British state-owned company, and it extends our emissions around the world. It must be stopped – wherever BP goes, protest will follow.

• Farhana Yamin is a climate change lawyer and a coordinator of Extinction Rebellion’s international solidarity network