The ornamental Denton Gardens lies to the east of the pier and south of Brighton Road and features a seafront shelter.
It was gifted to the town in 1922 by former mayor James Gurney Denton.
Campaigners are currently fighting against plans to convert the site for commercial uses.
This follows Worthing Borough Council’s promotion of the site for use as an adventure golf course and café.
Representatives from the Friends of Denton Gardens and the Worthing Society were at the full council meeting on Tuesday (December 14) to ask what future plans hold for the gardens.
Annie Waran, from the Friends of Denton Gardens, said: “As we approach the centenary of alderman Denton’s gift to the people of Worthing, it is time to listen to the 1,200 petitioners, the recently constituted Friends of Denton Gardens group, the Worthing Society, Central ward councillors and our local MPs, all of who urge that the unique walled Denton Gardens and the shelter be protected, and their historic character maintained.
“Will [the council] now assure us that the unwelcome attempt to further extend the commercialisation of the gardens and shelter be dropped?”
The Worthing Society’s Susan Belton added: “Our heritage assets are an irreplaceable resource.
“The current offer of a lease to allow increased commercialisation of the gardens with the associated significant alterations should be immediately withdrawn.”
Council leader Kevin Jenkins (Con, Gaisford) replied: “We’re fully committed to retaining and celebrating the town’s heritage but we’re also aware of the need for the town to move forward and to evolve to ensure that Worthing becomes economically able to compete.
“It was also very interesting to read of the other voices that were expressing an interest in seeing an improved facility in that area, and as a council we have a duty to listen to all voices – nothing is ruled in and nothing is ruled out.”
Ms Belton asked if the gardens could be ‘naturally enhanced’ with a ‘limited golf experience’.
“This seaside garden in the 1930s was a unique area with many significant historic plants and it could again be so,” she said.
But Mr Jenkins pointed out that a part of the gardens is already a mini golf course and said that proposals were simply ‘expressions of interest’ at this stage.
It is understood that expressions of interest have been made to develop an adventure golf course and to convert the shelter into a café and the council leader promised a public consultation in due course.
Ms Belton said she ‘looked forward to a full consultation process’.