One of the UK’s most controversial art sponsorships will be thrust into the spotlight on Monday when Tate is forced to reveal the value of its longstanding relationship with the oil firm BP.

Tate lost an information tribunal case shortly before Christmas and was given 35 days to disclose the sums of BP sponsorship between 1990 and 2006. The deadline runs out on Monday.

Anna Galinka, of the campaign group Platform, which helped bring the case, said the figures were likely to be “embarrassingly small” and proof that Tate did not need to take the money.

Platform estimates that Tate gets £500,000 a year from BP, based on the £10m five-year sponsorship deal that was announced in 2012 by Tate, the British Museum, the National Portrait Gallery and the Royal Opera House.

“That represents around half a per cent of Tate’s operating budget and it is quite likely that the earlier figures are going to be even lower,” Galinka said.

“We are expecting these figures to show just how insignificant BP’s funding actually is. That the relationship is a lot more about politics, personal networks and BP buying cultural credibility than it is about actual money and actual reliance.”

The campaign against oil money being used to fund Britain’s cultural institutions comes at a critical time for the oil industry.

BP’s stock market value is a third less than it was before the Gulf of Mexico disaster in 2010, having been forced to sell off $40bn worth of assets to pay fines and compensation.

The collapse in the oil price over the last six months plus questions about the wisdom of BP’s 20% holding in Russia’s Rosneft group has left the city openly questioning whether the company could be the next takeover target.

But the wider concerns over BP, Shell and others are centred on a growing public debate about whether the core oil and gas extraction activities of these fossil fuel giants should be halted to help tackle climate change.

Ed Davey, the energy and climate change secretary, recently wrote to the Bank of England about the potential risk to pension funds of holding shares in the fossil fuel sector amid fears of a “carbon bubble” in overpriced assets.

A string of universities, pension funds, charities and businesses have pledged to disinvest from fossil fuel companies on the basis that such holdings are counter-productive to their aims to reduce global warming. The value of investments pulled out under the campaign so far is $50bn.

Critics say oil companies will find themselves cast as business pariahs if they do not change direction and move into low carbon energy production.

BP says it is proud of its long and well-established role of funding or partnering with the Tate, British Museum, National Portrait Gallery and the Royal Opera House.

“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,” a spokesman said.

Tate and other arts organisations have also stood by their relationship with BP, which sponsors the rehanged galleries at Tate Britain as well as the NPG’s annual portrait prize and the ROH’s Big Screens.

When the latest sponsorship deal was announced in 2011, the Tate director Nicholas Serota said trustees had thought very hard about it “and decided it was the right thing to do to continue with BP, who have been great supporters of the arts”.

A Tate statement said: “[BP’s] support has been instrumental in helping Tate develop access to the Tate collection and to present changing displays of work by a wide range of artists in the national collection of British art.”

Monday’s revelation represents the latest chapter in a drawn out case. It was in April 2012 that Brendan Montague of the campaign group Request Initiative made an information request to Tate.

The tribunal ruling in December upheld some of Tate’s redactions and commended them for being open and thorough. But, crucially, it ordered the release of sponsorship figures between 1990 and 2006.

Tate’s submission included arguments that revealing more details would deter other sponsors and open them up to further protests.

Tate in particular has been the target of protesters, with the art collective Liberate Tate regularly staging interventions, the last being the unfurling of a giant black square in the Turbine Hall – referencing Tate’s redactions and the Malevich Black Square hanging a few floors up.

Galinka said one reason to focus on Tate was because “in many ways Tate is trying to be a progressive institution”. For example, it is part of the 10:10 campaign which encourages businesses, organisations and individuals to cut their carbon emissions.

“It is an organisation that has some commitment to values around justice and human rights and environmental responsibility. We see it as a contradiction that Tate can be part of 10:10 and funded by BP,” she said.

Tate, whose chairman is the former BP chief executive Lord Browne, has said it will not appeal the tribunal decision.