The artwork, which was discovered on the walls of Reading prison, depicts a prisoner resembling Oscar Wilde escaping from the facility using a string of bedsheets tied to a typewriter.
Winslet has joined calls to convert the old prison into an arts centre.
Speaking to the BBC, the Titanic star said that the “incredible Banksy piece of wall art” ought to remain and form part of the “legacy” of a new cultural hub.
“I just felt incredibly excited for Reading to have a Banksy,” said Winslet, who hails from the area.
“If Reading had a legacy space like that, to hand on to generation after generation, it could really be as valuable as some of those central London theatres.”
Next week, Reading Borough Council will submit a new bid to purchase the prison and convert it into a venue for the arts.
Banksy’s artwork alludes to Wilde’s internment in the prison between 1895 and 1897, which inspired Wilde’s 1898 poem “The Ballad of Reading Gaol”.
Some have interpreted the Banksy piece as an expression of support for the campaign to transform the jail into an arts hub, which has also been backed by actors including Dame Judi Dench, Sir Kenneth Branagh, Natalie Dormer and Stephen Fry.
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