A new pressure group called the Speakers' Corner Movement, which has the backing of veteran orators Tony Benn and Lord Soper, says the Royal Parks Agency is obsessed with "revenue raising" schemes.
The campaigners have also criticised Royal Parks Enterprises, which generates income for the Royal Parks Agency, for putting a carousel on the Speakers' Corner site, "driving out" speakers and failing to promote the future of Britain's living monument to democracy.
The site has attracted many influential figures since it was designated as an area for free speech by an Act of Parliament in 1872. However, Heiko Khoo, who founded the Speakers' Corner Movement, says this tradition could disappear under the management of Royal Parks Enterprises, which won its five-year tender last year.
"Speakers' Corner is the most famous place in the world for democratic rights. It's an equivalent to the Statue of Liberty," said Mr Khoo.
His views were shared by the MP Tony Benn, who memorably read the banned book Spycatcher at Speakers' Corner.
"It's the principle that you can get up and say what you think, which is not popular in the Labour Party or anywhere else these days," said Mr Benn.
Lord Soper, 95, has preached in the park since 1942 and says he intends to carry on: "It should be protected for the people."
Tom Corby, a spokesman for the Royal Parks Authority, denied the site was under threat but did admit its priority was to raise income from the park with ideas such as the carousel.
He dismissed plans for public ownership but said the Royal Parks Authority was willing to consider other proposals.
"The park costs millions to run," he said. "The carousel occupies a tiny corner and to say that this interferes with freedom of speech is a ludicrous claim. It's only there for the summer."