From my experience, Section 106 agreements are a legal contract signed prior to the grant of planning consent and are more or less set in stone. Unless the agreement specifically provides for amendment by one party and not the other(s), any subsequent re-negotiation might invalidate the original agreement.
If the agreement provides a sum of money for quantified, categorised, but non-specific sums (e.g. £500k for education), it is for the recipient authority to determine how the money will be spent. In the case of a parish council, this would be included in their normal budgetary process.
One of the leading concerns in my area with S106 is that it is enforceable only against the original parties to the agreement. If a developer sells a plot with planning permission before commencing development, it is virtually impossible to enforce the S106.