Rural development grants and Countryside Stewardship applications appear to be on hold following the referendum on 23 June.
Michael Asbury, chairman of a charity that runs Pewsey Heritage Centre in Wiltshire, applied for a grant to convert a local building into a research and education facility.
The grant of £7,500 from the LEADER programme was initiated in March, said Mr Asbury.
Hoops were successfully jumped through, reams of paper forms filled in, and the grant application was submitted to the reviewing board at a meeting on June 24, he said.
Weeks later, Mr Asbury said he was still waiting to be told whether the application was successful.
The ongoing delay prompted Mr Asbury to write to the Daily Telegraph saying he understood that "decisions were made and grant funding may or may not have been awarded".
In the letter, Mr Asbury said he was told an embargo had been put on the results of the application by Defra's Rural Payments Agency.
"I was under the impression that until Article 50 of the Lisbon Treaty was invoked, relations between Britain and the rest of the EU should continue as they are," he said.
"They obviously are not.
"Based on the performance of the Rural Payments Agency, it is not European bureaucracy that we should be afraid of in any Brexit negotiations, it is our own dear civil service.
"Frightened of its own shadow, it seems completely unable to make constructive and beneficial decisions."
The National Farmers Union has also complained that its members are being left in the dark over whether Countryside Stewardship applications will be honoured.
The stewardship payments reward farmers who undertake environmental measures on their land.
The Daily Telegraph has now published an article headlined "Farmers and rural business in limbo amid Brexit cash freeze".
A Defra spokeswoman told the newspaper: "The government recognises the need for certainty when it comes to EU-managed projects and will make an announcement in due course."
She added: "We will do what is needed to support our farmers as we leave the EU and make a success of Brexit."