Sir Elton John, Liam Gallagher and Nicola Benedetti are among 110 artists who have signed the open letter.
It said they had been "shamefully failed" by the government over post-Brexit travel rules for UK musicians.
On Tuesday, the government confirmed it had turned down an EU offer that would have enabled frictionless touring.
Culture minister Caroline Dinenage said the EU's "very broad" offer "would not have been compatible with the government's manifesto commitment to take back control of our borders".
