Spike Island, a contemporary art centre in Bristol, recently funded solar panels, but say the new levy could add more than £1,000 a year to their electricity bill.
Kate Ward, deputy director, said rising electricity costs will “prevent us from switching to low-carbon heating like heat pumps, increase our running costs and put our work with artists at risk”.
Ms Ward added the government “needs to rethink how they approach electricity bills to make it viable for more charities and small businesses to make the right decisions for the planet”.
Sizewell C is being built over the next 10 years and will cost £38bn to build, it will supply electricity to the equivalent of six million homes for at least 60 years.
The government spokesperson said it is part of its clean energy “superpower mission”, which is the only way to bring down energy bills for good and “will also secure thousands of good, skilled jobs and billions in investment”.
