The agency says it spends up to £50,000 removing shingle from the mouth of the river - and that climate change, sea levels rising and past interference by man have put the Cuckmere estuary under increasing pressure.
It stated this week it will wit
hdraw maintenance - after a two-year notice period - of the river banks below Exceat Bridge.
This will result in the banks, which are near the end of their useful life, failing over time and the area reverting to an intertidal estuary.
Andrew Pearce, Environment Agency area manager for Kent and East Sussex, said, "We believe there is a better way to manage this special place.
"Climate change is presenting us with many challenges and the way we manage flood risk here has to change.
"Restoring the Cuckmere estuary to a tidal floodplain will allow the area to adapt to climate change and will bring with it great opportunities and benefits for visitors and wildlife.
"This is a beautiful landmark and an undeveloped area and it wouldn't be right to continually build bigger defences here.
"Our decision will not increase flood risk for any properties in the Cuckmere River catchment. "But it will save valuable flood risk management money which can then be directed to where it is most needed to protect people and properties."
However, a partnership of local councils, heritage and conservation agencies have joined forces to protect the Cuckmere Estuary, and will be seeking the views of residents and local businesses about its long-term future.
The Cuckmere Estuary Partnership favours a more managed approach. This would mean that access and recreation in this popular local area could be maintained, while allowing the gradual return to a naturally functioning estuary system.
Working with nature in this way would enable the partnership to plan for change and to optimise the benefits for people and wildlife, said a spokesperson.
Kate Cole, of the Cuckmere Estuary Partnership, added, "We can't ignore this problem. The current defences are reaching the end of their natural life, and water levels already reach the top of the banks at high tide.
"Our current thinking is that a managed realignment process would be best for wildlife, residents and visitors, and the local economy.
"It would allow footpaths and other amenities and management measures to be put in place before any major natural changes that may occur, and would enhance the outstanding natural beauty of the region.
"We recognise that the Environment Agency is unable to spend flood risk management money on this.
"Our aim is therefore to work together with the community to review the options, to develop the best possible outcome for the estuary, and to then attempt to find alternative funding to make it happen.
"Over the coming months we will be talking to residents, local businesses and others about the future of the estuary, as well as launching a website for people to share their views.
"We want everyone to be able to have their say, and we urge anyone with an interest in the issue to contact us to find out how they can be involved."
Local MPs have spoken out against the Environment Agency's decision.
Lewes MP Norman Baker said, "The Environment Agency is an unelected body and therefore has no popular mandate for the controversial course of action it wishes to pursue. They may well feel they have a good case, but then experts on the other side of the argument feel likewise.
That is why I have long argued that the proposal to allow the estuary to flood must be subject to some sort of external validation by an independent element, perhaps through a public inquiry. It is highly regrettable that the Agency has not accepted the need to do this. Their actions, in ploughing ahead with such a controversial move without such a process, make it less likely local people will simply accept the decision, and more likely that a legal challenge will result.
"Even at this stage, I call upon the Agency to think again. If their case is as strong as they think it is, and they do have a case, then they should be prepared to argue that before an independent decision-making body."
Eastbourne MP Nigel Waterson said, "Unfortunately the Environment Agency seem determined to abandon this very special area to the sea.
"They have not provided the detailed results of the consultation and I demand that they are published; but we do know that this unique natural feature is hugely popular with local people and visitors alike.
"They claim that nothing will happen immediately. But in the same breath they say they will not repair damage caused by severe storms.
"One such storm could weaken the existing defences to such an extent that the sea could pour in. And there is a real risk of the A259 being cut by flooding.
"I continue to be totally convinced that the only way to ensure popular supprt for these plans is to hold a proper public inquiry, where both sides of the argument can be heard."
Anyone wanting to share their views with the the partnership should call 874302 to register their interest.