It's highly desirable to have rules! They provide protection for the clerk as well as the council, as the clerk should not be placed in a position where there can be suspicion of wrongdoing. My opinions in more detail are as follows, and I believe they are in line with the standards required for local council finance.
Cash is best handled by an "imprest" system. That involves starting with a set sum of money, say £100. As it is spent, so receipts etc accumulate. At any time, the sum of receipts plus cash would be exactly £100. When the cash gets low, an amount of cash equal to the sum of all the receipts is withdrawn from the bank and the receipts filed. That restores the cash balance to £100, and so the process goes on. Working in this way, it is possible to have a spot check at any time that cash plus receipts add up to the set figure.
In general, purchase accounts should be settled by cheque, with the requirement for two councillor signatures. Many councils have relaxed this provision so that, for example, regular utility bills can be paid by direct debit. However, it is excessively lax to allow payments solely on the authorisation of the clerk, who should not be an account signatory.
While it is desirable to delegate enough responsibility to the clerk to avoid excessive involvement in detail by the council, there must also be effective control procedures. It is important that there should be an effective programme of councillor audits.