Campaigners are demanding an urgent meeting with Kirklees Council over the future of the vandal-hit chapels in Dewsbury Cemetery.
Council chiefs announced this week that one of the listed Twin Chapels at the entrance to the cemetery is to be made safe.
Both chapels, which date back to 1859, are derelict and in a state of decay but one of them was further damaged by storms in February.
The council says it will shore up the damaged building in the next few weeks but a new campaign group wants a long-term solution.
Simon Reed, co-chairman of the New Friends of Dewsbury Cemetery, accused the council of neglecting the chapels, adding: “These are listed buildings and the council, as the owner, has a duty to protect and maintain them.”
Mr Reed, 37, who has family graves in the cemetery, welcomed news that one of the chapels was to be made safe but said he wanted both to be made weather tight.
“Both chapels are crumbling and there are holes in the roofs,” he said. “The least the council can do is save them from further damage and show they care. Hopefully the chapels can be restored at some point in the future.”
The new group aims to continue the work of a long-established Friends group, which has campaigned tirelessly for restoration of the chapels.
“We have spoken to Kirklees and they promised to meet us but then it all went quiet,” said Mr Reed. “It’s very deflating.
“We just hope the council will work with us and not against us.”
The group is also concerned at the rundown state of the cemetery generally.
Many of the older graves have been damaged with stones laid flat for safety reasons.
The cemetery, off Heckmondwike Road, is also a magnet for anti-social behaviour with drunken louts intimidating people visiting graves.
Mr Reed said the group planned a leaflet campaign to raise awareness and would also produce a video showing the neglect and include interviews with local people.
In a statement a council spokesman said the roof of the damaged chapel was to be removed and the rest of the building made safe.
He added: “The works, which are likely to start in the next few weeks, will be carried out in consultation with the council’s conservation officers and are estimated to take a week to complete.
“Both buildings have been fenced off to prevent unauthorised access and secure the sites.
“Slates removed from the chapel will be stored for potential future restoration.”
The spokesman said the council was “keen to work with any local community group to determine a practical way forward for the chapels and the cemetery.”
The council could not say whether work was to be carried out on the other chapel.
Previous attempts to secure Lottery funding for restoration came to nothing.
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