School climate protesters who took to the streets in huge numbers across the UK last week are threatening to boycott the Royal Shakespeare Company over its sponsorship deal with BP.

In a letter being sent to the RSC on Thursday, a group representing young people in towns and cities across the UK, says it will launch a boycott campaign unless the theatre company severs its ties with big oil.

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The move comes amid growing concern among young people over the escalating climate crisis. Last week, millions of children took part in the global climate strike and this week the Swedish teenager Greta Thunberg excoriated world leaders at the UN headquarters in New York for their “betrayal” of young people.

BP sponsors the RSC’s £5 ticket scheme for 16- to 25-year-olds, but the school strikers say the theatre company’s tie-up puts young people in an impossible position.

“If we, as young people, wish to see an affordable play at your theatre we have to help to promote a company that is actively destroying our futures by wrecking the climate,” the letter says.

“As an organisation that appears to care about climate breakdown, it simply makes no sense for you at the Royal Shakespeare Company to be accepting sponsorship from a company that is the third biggest corporate source of greenhouse gases in history.”

The pressure is growing on arts institutions to sever their ties with fossil fuel firms, and this year there have been a series of protests by artists and campaigners at UK cultural institutions such as the British Museum, the National Portrait Gallery and the Natural History Museum.

In June Mark Rylance, who had been an associate artist with the RSC for 30 years, resigned from his position saying BP’s sponsorship deal allowed the company to “obscure the destructive reality of its activities”, which he said threatened the future of the planet.

School strike organisers say the RSC “needs young people far more than it needs BP, with children and young people making up the bulk of the audiences of its hit show Matilda the Musical”.

Eden, a 19-year-old student at the Royal Central School of Speech and Drama in London, is one of the organisers who has signed the letter.

“Shakespeare said ‘the great globe itself shall dissolve’. By endorsing BP, the RSC is allowing his words of the past to become a horrifying reality. Continued support of the oil industry will not only destroy my future, but is already causing terrible suffering to people on the frontline of the climate crisis right now,” Eden said.

“How can you sleep at night knowing that you’ve tied the purity and hope of the arts to BP’s dirty, colonial extractive practices?”

Catherine Mallyon, the RSC executive director, and Gregory Doran, the artistic director, said: “We welcome the conversation around this issue and will respond once we receive the letter. We recognise the importance for a continuing, robust and engaged debate, we acknowledge the climate emergency and recognise the strength of feeling especially amongst our young people.

“Our work with over 500,000 students annually means their feedback and opinions are very important to us. This subject is very much live at the RSC with our artists, staff, board and our audiences and we look forward to reviewing the contents of the letter.”

A BP spokesman said: “BP has been supporting the arts in the UK for over 50 years and our support allows the institutions we partner to widen access and extend the reach of their productions and exhibitions.

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“Our position on climate is clear – the world is on an unsustainable path and needs to move to net-zero carbon emissions in the decades to come. Everyone will have to play their part in addressing this challenge: individuals, governments and companies such as BP.

“We are investing to grow low carbon businesses and activities and working and investing in our other businesses to reduce emissions from our operations.”

Jess Worth, co-director of the campaign group Culture Unstained, which has been spearheading the campaign against fossil fuel involvement in the arts, said the move by young activists was a significant blow to the theatre company.

“This is another example of young people finding their power and using it to create change in institutions that, until now, have taken their concerns for granted,” she said.

“Education and schools work is one of the RSC’s priorities, and an important source of income. This is a chance for the RSC to demonstrate how much it values young people, by not just listening but acting on their passionately held concerns.”