Artist and judge of this year's Portrait Award by BP, Gary Hume, has said it's time to look elsewhere for sponsorship of the BP Portrait Award.
The National Portrait Gallery prize has been sponsored by BP for 30 years but the energy company has faced growing criticism over environmental issues.
Hume told BBC Radio 4's Today programme that BP "was now a problem".
In a statement, the National Portrait Gallery said BP's support "enables free admission for the public".
With the winner of the prize due to be announced later on Monday, Hume told Radio 4: "It's a good moment to say it because it's the day of the announcement.
"It will focus people's minds on exactly on who is sponsoring and who has been sponsoring for many years."
He said he didn't take part in choosing the winner and that he decided to voice his views following the recent Extinction Rebellion climate change protests.
"I was very moved by Extinction Rebellion. It woke me up. I thought it's about time for me to actually do something, too.
"After the judging, I decided to write to Nick [Cullinan, director of the National Portrait Gallery] to say BP was now a problem. BP has been a solution in the 20th Century, and in the 21st Century, it's a problem."
He added: "BP could continue to support the National Portrait Gallery without putting their name anywhere, it could be an anonymous gift.
"Without the institutions such as BP making a concerted effort... we haven't got a chance."
When asked how hard it would be to find another sponsor, Hume said: "I think it would be difficult, it's always difficult, and with Brexit, it's incredibly hard to raise money.
"It's not going to be simple but I'm afraid sometimes you have to pay the price."
He said he would be willing to sacrifice the prize but added: "I don't think it will come to that."
The National Portrait Gallery statement read: "The National Portrait Gallery respects other people's rights to express their views and we are grateful to all the artists and judges who have contributed to our annual Portrait Award, which represents the very best of contemporary portrait painting by artists from all over the world.
"While partly supported by grant-in-aid from government, which accounts for 33% of total income, the National Portrait Gallery works with a wide range of companies in support of its exhibitions and displays.
"The sponsorship of the Portrait Award by BP is now in its 30th year. This support directly encourages the work of talented artists and helps gain wider recognition for them and enables free admission for the public, over 275,000 visitors in London last year.
"Since 2010, BP has also given special support to the BP Portrait Award: Next Generation programme which encourages 14 to 21 year olds to become involved in painted portraiture."
The BBC has also contacted BP for comment.
BP shareholders overwhelmingly voted for a climate change resolution at the BP's AGM last month.
The resolution, which was proposed by a group of investors called Climate Action 100+, will mean the oil giant must set out a business strategy consistent with the goals of the Paris Agreement to keep global warming to well below 2 degrees centigrade.
Several other artists, including previous winners of the BP Portrait Award, also wrote a letter to Cullinan requesting that the gallery ends the sponsorship deal with BP, including Wim Heldens and Craig Wiley.