Vixen Tor has been closed to the public since May 2003
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About 50 people took part in a demonstration on Saturday in protest at a famous South West landmark being closed to the public.
The British Mountaineering Council went climbing on Vixen Tor on Dartmoor despite it being private property.
Its owner Mary Alford ended access to the tor in 2003, saying she feared being held liable for accidents.
She has said she would reopen it for a one-off payment of £30,000 and a yearly sum of £35,000 and insurance costs.
Sphinx of Dartmoor
Dartmoor National Park Authority (DNPA) says access payments are usually about £1,500 a year.
Protesters say DNPA should use its compulsory purchase powers to buy the land, which was open to the public before Mrs Alford became the owner.
Mrs Alford put up barbed wire fences and Keep Out signs on the land after 30 years of public access to the Tor, known as the Sphinx of Dartmoor.
It was then listed for public access under the Right to Roam legislation, but the owner appealed against that and won.
One climber Haggis Harris said: "It used to be enjoyed not just by local population but the many visitors to the moor, probably over generations.
"The Countryside and Rights of Way Act has failed to get access back for us, so I'm hoping the DNPA will use their powers to buy back the land so we can all enjoy it again."
Mrs Alford was unavailable for comment on Saturday.