Shell is to end its relationship with two of the UK’s leading arts institutions amid growing concern about big oil’s role in the escalating climate crisis.

The fossil fuel corporation has confirmed it is not renewing its corporate membership deals with the Southbank Centre and the British Film Institute (BFI) when they come up for renewal later this year.

Campaigners say the decision underlines the shrinking “social licence” of fossil fuel companies in the midst of the climate crisis. It follows similar moves by the Royal Shakespeare Company (RSC), National Theatre and National Galleries Scotland, which have all severed ties with major oil companies in the last year.

Chris Garrard, from the campaign group Culture Unstained, said the end of Shell’s involvement with the BFI and the Southbank Centre was a crucial milestone in the campaign.

“From its HQ on the South Bank, Shell has pursued a business plan that has trampled indigenous people’s rights and pushed the world deeper into climate crisis,” said Garrard. “Meanwhile, it has sponsored its cultural neighbours as part of a cynical attempt to deflect attention from the damage it was causing. But the show is over for Shell.”

A spokesperson for Shell said the decision not to renew the contracts had been taken last year and mutually agreed with the Southbank and the BFI. “Last year we decided not to renew annual memberships with the BFI or the Southbank Centre, collectively worth around £20,000, when they expire later this year,” it said.

The BFI confirmed it had been Shell’s decision. Harriet Finney, the BFI’s director of external affairs, said the institute was “committed to supporting a sustainable future”.

“We are in the process of reviewing the impact of our own activities across all our sites; how we can better support the UK’s screen industries to move towards sustainable practice and how we respond culturally to the climate and ecological emergency.”

The Southbank Centre has had a relationship with Shell stretching back to 2006 and lists the company as a partner on its website. A spokesperson said the decision to end the two-year corporate membership had been mutual and declined to comment further.

The leading tenor Mark Padmore, who will perform at the Royal Festival Hall in October, said he was delighted with Shell’s decision.

“Today, more than ever, we all need to examine our way of life and the implications of our actions, as we respond to the growing climate emergency,” he said. “Making beautiful music does not excuse us from seeking to understand how our work is funded and asking questions about the kind of unsustainable businesses those partnerships might promote.”

Last year, the actor Mark Rylance resigned as an associate artist with the RSC after 30 years over its sponsorship deal with BP, arguing it allowed the company to “obscure the destructive reality of its activities”. A few months later, the RSC announced it was cutting its links to BP after a “careful and often difficult debate” internally.

The latest move increases pressure on other arts institutions such as the British Museum, National Portrait Gallery and Science Museum Group, which have all faced criticism over their oil sponsorship deals in the past 18 months.

Last month, the activist theatre group BP or not BP? occupied the British Museum for three days, sneaking a “Trojan horse” into the courtyard and staging a mass protest in the museum involving 1,500 people.