It's a good question, but I have to side with Mrs Abster in citing the electorate as the main practical answer. Questions about the "policing" of parish councils crop up regularly, and there are certainly abuses. But as there are a great many parish councils (including town councils) the feasibility of a supervisory regime is questionable. Even when the English Standards Board was operational, its proceedings were slow, its sanctions were often mild, and it struggled to cope with numerous minor complaints.
Ultimately, it is indeed up to the electorate to take an interest in their councils and to put up and elect new candidates where there is a need for improvement. In between elections, councillors can sometimes be influenced by adverse publicity. Where a council is operating improperly, it may be possible to involve the auditor. References to the Monitoring Officer (usually senior legal officer of the district council) can be made, but there are no teeth to any decision. In extreme cases, the criminal law comes into play, but that is very unusual.
You could argue that it is difficult to get electors to engage. That is true, and my personal opinion is that all our democratic institutions need to be refreshed. There is a need for less centralisation and for more engagement with electors at all levels of government. While district and county councils are hamstrung by central government, it is difficult to generate much interest in their proceedings. It also seems true that they are happy to evade scrutiny by electors whenever possible. It won't be easy to change this situation.
So it seems that there are inherent limitations in the supervision that could be applied to parish councils. Nonetheless, it does seem that the vast majority of parish (and town) councils operate conscientiously in the interests of their citizens. They provide a valuable channel for local action and for representations to the larger authorities. The benefits seem to greatly outweigh the drawbacks.