More than 80 performers have signed the letter, with Derry Girls actor Siobhán McSweeney saying she was "deeply worried" that the government was lagging behind.
"There is a way to work alongside AI and to use it as a tool that benefits us rather than rendering us obsolete," she said.
"Our audiences want that human connection. Not AI."
As well as actors, other signatories include those working in other performing industries.
That includes Scottish singer Sandi Thom, known for her 2006 hit I Wish I Was a Punk Rocker (With Flowers in My Hair).
She said she was signing the letter because her voice was "unique to me and was handed to me at birth".
"Behind that voice is the emotion, the life, the pain, the tears and joy that I've felt along the way," she said.
"Without creativity, we are nothing."
It comes a few months after lawyers warned UK legislation has become "unfit for purpose" because of the advancements of AI tech.
"The law comes close, but it doesn't fully protect your voice, your face or your identity," Dr Mathilde Pavis said in June.
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