Bourne Preservation Society asked Bourne Town Council for £40,000, which it believed had been set aside for the restoration of the chapel in the town's cemetery.
The society was banking on the cash to begin restoration work to make the chapel watertight before winter and needs to conduct two surveys in order to apply for funding.
The council has put £40,000 in a cemetery development fund, for extending and improving the burial ground, but says it was never said this was for the chapel.
But councillors refused to hand over the money during a finance and general purposes committee meeting on Tuesday.
Coun Mark Horn said: "We are not going to spend council money on the chapel. It was put forward to us that they were going to raise the money on their own.
"We said that we would put money in after they had hit certain milestones.
"We said there would be a timeline. The proof of whether they can raise the money is in the pudding."
Coun David Higgs said: "We did a survey and the people of Bourne were clearly against spending any money, which is why the chapel has gone to the preservation society."
Coun Trevor Holmes put forward a proposal.
He said: "There has been no money specifically allocated to the chapel of rest, but there has been sums allocated to the cemetery.
"I would like to see us look to a sum of a maximum of £10,000 to be spent on necessary expenditure over the next six or 12 months."
Coun Jane Kingman-Pauley said: "I think we have got to help the Bourne Preservation Society to go forward. They are doing a lot of fundraising and they are working very hard."
The proposal was shot down, after three voted in favour of it and four voted against.
However, this decision is only a recommendation to full council as the committee has no power to make a decision on council funds.
The town council agreed to hand over the chapel to the Bourne Preservation Society in June and is drawing up a legal agreement, which both parties have to sign.
After the meeting, society chairman Jack Slater said the group was "down, but not out".
He said: "Clearly we are disappointed about tonight's vote and we will be taking every action within our power to ensure the town council carries out repairs on the chapel, which will cost them a lot more than that decision.
"We are not giving up."
Full council will look at the request at its Tuesday, August 5, meeting at the Bourne Corn Exchange.