The oil giant gives £2m a year to four of the country's top cultural institutions. Environmental groups say this is "inappropriate" given its involvement in fossil fuels, which intensify global warming.
In recent months BP has also faced protests at the other two sites where it holds partnerships, the British Museum and the National Portrait Gallery, but says it wants to continue with "community" engagement. It is expected to be one of many targets for criticism at a climate change rally in London on Sunday.
Last Wednesday 14 dancers staged a protest against BP by performing a routine in front of a crowd of thousands in Trafalgar Square who were watching a live stream broadcast of the Royal Opera House's production of Verdi's Rigoletto.
The dancers – calling themselves BP Out of Opera - were dressed in black with masquerade masks on their faces and green BP logos on their bodies.
The following day, the Tate link with BP was in the spotlight at an information tribunal in London over the art institution's unwillingness to provide specific financial details of its commercial partnership with the oil group, whose reputation is still tarnished by the Gulf of Mexico oil spill four years ago.
A group known as Request Initiative, working with the oil protest group Platform, made a legal challenge claiming the Tate was using information law to unfairly withhold information.
"There's a clear public interest in knowing exactly how much money Tate is getting from BP. Gallery-goers want to know if the amount of money involved justifies Tate's complicity with one of the companies most responsible for destroying a stable climate for generations to come," said Kevin Smith, an oil sponsorship campaigner from Platform.
Rosa Curling, a lawyer from the solicitors Leigh Day involved in the case, added: "The fact BP has not consented to this information being revealed should not discourage Tate from doing the right thing. They should not be held hostage by their corporate sponsors in this way."
The art institution, which faced an anti-oil protest at its Tate Modern premises earlier this month, said it did not want to comment on the case. "The information commissioner decided that some of the information is exempt from disclosure under the Freedom of Information Act and some is not. Both decisions are subject to appeal - the first by the requester, the second by Tate. Because the appeal proceedings are ongoing we will not be making any further comment at this stage," it added. A final ruling on the case is not expected for a month.
BP, whose former chief executive Lord Browne is chairman of the trustees at the Tate, also declined to comment on the legal case on the basis that it was not a direct party to the action. "We are aware that some disagree with our support for these institutions. But as a major company headquartered in the UK, we believe it is right that we contribute to the wider community, and not only through our business activities," it said.
BP said having long-term relationships with the likes of the Tate that had run for many years helped to develop strong partnerships that were beneficial to both sides.
"They support the institutions' long-term development of programmes of exhibitions and performances, helping them to secure exhibits, performers and artists well into the future, and helps allow people around the country and internationally to experience outstanding exhibitions and performances from our partners. And BP also benefits, allowing us to build relationships, host events and engage our staff."
BP is not the only oil company to face protests. Shell found itself on the end of criticism when it was a sponsor of the wildlife photographer of the year competition at the Natural History Museum. Climate campaigners in the US have also previously targeted action against the Koch Brothers over their investments in oil but sponsorship of the arts.
Energy industry executives say the demonstrations are generally undertaken by a very small section of the community but activitists believe they can make oil as unpopular with sponsors as tobacco.
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