Almost 90 prominent figures signed a letter claiming that such a sale would be "misjudged and short-sighted".
The long list of concerned celebrities, politicians, media figures and others includes artist Tracey Emin, model Lily Cole, chef Hugh Fearnley-Whittingstall, former mayor of London Ken Livingstone, novelist Julian Barnes, actress Gillian Anderson, broadcaster Dame Joan Bakewell, actor Richard E Grant and designer Dame Vivienne Westwood.
The letter by the Save England's Forests campaign said a Bill being debated in Parliament would allow the Government to sell the entire public forest estate to commercial interests on the open market.
It also expressed fears that over time, access to currently public woodland would become limited and its protection eroded.
The campaigners wrote: "We are an island nation yet more people escape to the forest than to the seaside.
"Our forests nurture countless species of native plants and wildlife. We have relied on them since time immemorial yet we are only a heartbeat in their history...
"We, the undersigned, believe it unconscionable that future generations will no longer enjoy the guarantee of a public forest estate."
They urged the Government to suspend any significant sales "until the public has been fully consulted".
They added: "We expect our leaders to engage in real dialogue with communities throughout the country to create a sustainable future for our public woods and forests."
The campaign was launched in response to the Government's announcement last year that it was consulting on "new ownership options" for the public forest estate.