Oil giant BP is to cut its cultural sponsorship funding by £2.5m.
It has pledged £7.5m over five years to the Royal Opera House, British Museum, National Portrait Gallery and Royal Shakespeare Company from 2018.
It had sponsored the first three, plus Tate Britain, for £10m in five-year deals running up to 2017.
A BP spokeswoman said due to "cutting costs and reducing staff numbers... we could not continue all of our sponsorships at the same level".
The company announced in March it would be ending its 26-year association with Tate Britain in 2017.
In April, several famous names including actors Mark Rylance and Emma Thompson and Shadow Chancellor John McDonnell asked the British Museum to drop BP as a sponsor, claiming the company was "using its influence to lobby against effective climate policies".
The following month, campaigners disrupted the launch of a BP-sponsored exhibition at the museum.
British Museum director Hartwig Fischer said 20 years of BP support had "enabled the museum to host magnificent exhibitions and events with a great public benefit".
"These events have been enjoyed by millions of visitors and have deepened understanding of the world's many cultures and their interconnectedness.
"The museum is grateful to BP who have confirmed they will continue to support the British Museum exhibition programme for a further five years."
The BP spokeswoman said the decision to cut sponsorship was due to a fall in oil and gas prices and not because of opposition from campaigners.
She added the industry was "going through a period of rebalancing, but our commitment to the UK and to our partners is for the long-term".