Fellow resident Ruth Kent said she was feeling “distressed” at the thought of having to move after 20 years.
She said: “We don’t have home anywhere else. We love our home, and we want to stay in our homes.
“We are having to get our heads around the idea that this might not continue much longer. We are quite distressed about it.”
Woodcot was given grade-II* listed status in 1949, according to Historic England, external.
The council said the property was gifted to a charity by its owner, Elizabeth Jennings, in 1969 to give older people without homes somewhere to live. The charity handed it onto Age UK in 1977.
Campaigner Kathy Koo, who knew Ms Jennings, said she would have never left the property to charity if she thought it would be sold.
“She wanted old people with a connection to Salcombe to benefit from living in this beautiful place,” added Ms Koo.