The union was reacting to the news that the Science Museum Group is looking at introducing charges or closing one of the National Railway Museum (York and Shildon), National Museum of Science and Industry (Manchester) or National Media Museum (Bradford).
National Secretary Alan Leighton said: "Unfortunately this is not an isolated issue. After cuts of 15% in 2011, and further cuts to cash baselines for 2013 onwards, all national museums, galleries and other bodies sponsored by the Department for Culture, Media and Sport are now being asked to consider how to cope with further cuts of 5%, 10% or 15%.
"These organisations have already implemented substantial cuts to their activities, including significant job losses and pay freezes. Further cuts of the magnitude suggested are bound to make organisations consider introducing charges and closing museum branches or floors – which the public will see as unacceptable.
"The financial logic for such cuts is baffling, given that every £1 spent on the arts generates £4 for the economy. We are talking about organisations that make a major contribution to the UK by enabling people to develop an interest in and an understanding of science, technology and the arts. The Government is abrogating its responsibility. It's all very well telling museums that how they spend their money is their choice, when cuts have limited their options so dramatically."
Leighton called on the Government to drop its plans to further reduce funding in this area, including possible plans to close down the DCMS. "Instead, it's time to begin a programme of reversing the cuts and using the creative industries to kickstart the economy."