Galapagos Islands Tourism facts
Speaking at a dinner at Christ's College, Cambridge, to mark the 200th anniversary of Darwin's birth, Mr Marr warned that the islands' habitats face ruination unless human development leaves space for the wildlife.
Mr Marr first visited the islands to research Darwin as part of the BBC's Great Britons series and has since become an advocate of the World Heritage Site.
But he said visits, that are already controlled by the Galapagos National Park, should be limited to once in a lifetime.
"The Galapagos islands are truly astonishing – home to many unique species, " he said.
"But they are very delicate, and there is huge pressure on them because of tourism, development and the introduction of invasive species. That is why, having been to the islands once, I promise never to go back."
Charles Darwin found a host of unusual animals on his visit to the archipelago on the HMS Beagle in 1835, including the famous giant tortoises.
But he also brought the first invasive insects and animals that have gradually been eroding the natural flora and fauna ever since.
Black rats and goats have been particularly damaging to the environment but perhaps the most invasive species of all are humans.
There are 106 species on the islands and in the surrounding waters, out of around 450, that are now considered endangered or critically endangered, while another 90 have been officially declared as vulnerable. Some species of the giant tortoise and the Galapagos mouse have disappeared completely.
Sir David Attenborough, who is also due to speak at the dinner, last visited the Galapagos Islands on his 80th birthday.
Events around the country today are due to celebrate the birth of Charles Darwin. HRH the Duke of Edinburgh is due to unveil a new statue of Darwin at Christ's College and a series of free public events are being held at the Natural History Museum in London.
Toni Darton, Chief Executive of the Galapagos Conservation Trust, hoped the celebrations will help to boost funding for the huge amount of conservation work needed to ensure the species Darwin studied can survive another 200 years.
"Darwin helped to put the Galapagos on the map and now the huge interest in Darwin and the anniversary of his birth could ensure the islands' survival, " she said.