The 500-acre Dungeness Estate, in Kent, has been described as "Britain's only desert" by the Met Office.
The headland, which juts out into the English Channel, is a Site of Special Scientific Interest and has 29 homes built from railway carriages on it.
Maurice Ede, one of the owning trustees, said he had enjoyed running it but it was time to test the market.
The Dungeness Estate, which includes the cottage where film director Derek Jarman lived, has been part of a family trust since 1964.
Mr Ede said: "The trustees are getting older and the estate is in very good shape, it is profitable, so it's quite a good time to test the market.
"I have enjoyed running it, it has been great fun but I am not sure who would buy it."
Mark McAndrew, from estate agents Strutt & Parker, said the sale was incredibly unusual.
He said: "I've been doing my job for 28 years and I can absolutely hand on heart tell you I've never sold anything like this.
"The Met Office calls it Britain's only desert."
Mr McAndrew said the buyer could either be someone interested in conservation or looking at the beach as an investment.
He said the main income comes from EDF, which runs the power station, and use the shingle from the beach to protect it.
"They pay the best part of £100,000 per annum to move the shingle back to where it came from," he said.
"Obviously the power station needs protecting and will need protection for many years to come."
The Dungeness B power station, began generating electricity in 1983 and was scheduled for decommissioning 2018.
However, it will remain open until 2028 following £150m of extra investment.
A deserted shingle beach next to a nuclear power station has been put up for sale at £1.5m.