Yes, your Clerk is exceeding their authority. As a member of the public, you have the same rights and privileges as any citizen in a free democracy.
Looking at the churchyard issue, it seems unlikely that your district or county council will take on this responsibility without seeking reimbursement from the parish council. Assuming that the churchyard was formally closed by an Order in Council, the parish council had three months from the date of the Order to pass this responsibility to the district council. Beyond that deadline, the district council is entitled to refuse. Section 215(3) of the Local Government Act 1972 refers. If your churchyard wasn't formally closed, the maintenance responsibility lies with the parochial church council (or the diocese if the church itself has been closed) and the district council will not get involved.