Around 45,000 people have signed a petition calling for Wells Harbour Railway to be saved.
The campaign was started on May 1 by Ashley Illingsworth, 34, from Nottingham, who said it seemed "crazy" to shut down such a popular and important feature of the seaside resort town.
Mr Illingsworth, who said he had been on many family holidays to Wells over the years, said he felt he had to act after reading about the likely closure of the railway.
He said: "It seems a bit crazy to close it when so many people associate it with Wells. I don't understand the logic behind it.
"I'm not a local but always used to have family holidays in Wells and it brings back a lot of memories. I didn't expect there to be so many people who thought the same way.
"Maybe if there are enough voices behind the petition they will listen."
The miniature railway connects Pinewoods caravan park and the nearby Wells beach with the town centre.
The railway is owned by Gary and Alison Brecknell, on land owned by the Holkham Estate.
Last October the Brecknells told Holkham they wanted to stand down "in the next year or two" and asked for a new 10-year lease in order to sell the equipment to a new operator.
But a spokesman for Holkham said such a renewal would not be "ideal" as the area's needs were evolving.
The Brecknells have said the railway could close as early as this year as they would now have to sell the trains and specialised equipment as soon as a buyer came forward.
Neither Holkham, nor Mrs Brecknell, said they wanted to comment on the petition.
Mr Illingsworth said the support the petition had gained in under two weeks showed how important the railway was to Wells.
He said: "I had never thought before about how important it is for people who can't make the walk along the top to the beach.
"Every time I've been to Wells [the trains] seem full, so it's not like it's not well used. I wanted to show that I don't think Holkham should make this decision without consulting people, and not just the owners of the railway."
The petition can be found on change.org.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here