Keswick's Theatre by the Lake has unveiled plans for a £700,000 extension.
It wants to build a cafe with views over the nearby fells.
The theatre's managers say it would be the biggest development since it opened in 1999.
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Ransome's book, which tells the tale of four children who camp on an island in the middle of a Lake, has taken Keswick to the big screen.
Facts about the big cats that could soon roam Kielder Forest and the Scottish Borders.
Lynx UK Trust has chosen Kielder Forest, spanning Northumberland and the Scottish Borders, for a trial reintroduction of Eurasian lynx.