The appeal hearing at the Royal Courts of Justice in London into turning West Beach into a village green came to an end on Thursday February 28.
A decision is expected to be announced by the three judges overseeing the case in a few weeks.
Newhaven Town Council said if the appeal were successful it wanted to work with the port to reopen the sandy beach.
The appeal was against a judicial review held in November 2011, where it was decided that West Beach could not be registered as a village green.
Speaking after the court hearing, Newhaven mayor Graham Amy said: “We are hopeful that the outcome of the court case will be positive and that the appeal will be granted.
“If successful we would like to work closely with Newhaven Port and Properties to ensure that the beach is reopened to the mutual benefit of both the port and the people of Newhaven and in a way that does not adversely affect the operation of the port.”
The legal battle to get Newhaven’s sandy West Beach reopened to the public was taken to the Appeal Court last week, with the hearing lasting three days from February 26-28.
It was heard by Lord Justice Richards, Lord Justice McFarlane and Lord Justice Lewison.
The town council said the first day was devoted to arguments about the issue on which the Judicial Review was lost by East Sussex County Council in November 2011.
This was that registering West Beach as a village green would not be compatible with the statutory purpose (running a port.) for which the land is held by the Port Authority, because there is a conflict of statutory regimes.
The council said the three judges decided to reserve their position on this issue and asked to hear further arguments brought forward by the legal team for Newhaven Port and Properties on six issues they believed meant that the beach should not be registered as a Village Green.
On the second day these arguments from Newhaven Port and Properties were heard in detail.
After this the judges decided that they only needed to hear submissions from East Sussex County Council and Newhaven Town Council on two of these.
The third day was taken up with these remaining two issues, with the hearing finishing at about 2.30pm.
Newhaven Port and Properties said it did not wish to comment at this stage.
The decision will not be announced immediately – the judges in the case will consider their verdict and deliver it within the next few weeks.
At the review in 2011 it was concluded by Mr Justice Ouseley that the land could not be registered as a village green, because this would not be compatible with its statutory purpose (operating as a port).
The beach closed to the public in 2008 due to health and safety concerns from Newhaven Port and Properties, which owns the land, that it would be liable for any injuries which occurred on the beach.
Newhaven Town Council argued the beach had been used by local people for more than 20 years as of right for lawful sports and past times.