Environmental campaigner Save Surrey Countryside condemned the choice of site.
Its coordinator, Sally Blake, said: “We utterly condemn the decision… The destruction of this woodland is unthinkable vandalism at a time when woodlands are being planted and nature sites are being restored throughout the UK to combat our climate and nature crises.”
Blake said it was mature woodland, and a site of nature conservation importance, with free access to the public and a “much-used public golf course that was left to benefit of the people of Frimley in 1801”.
She said more than 11,000 people had already signed a petition to protect the woodland.
The trust said it would need approval from the Department of Health and Social Care to purchase the land.
Work on the new hospital is set to begin in 2028 or 2029.
In an interview with the BBC in January, former Health Secretary Wes Streeting confirmed the work was “fully funded”.
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