The problem is not with the councils having access
The problem is with the councils _ALLOWED_ to investigate in the first place.
It is _NONE_ of their f***ing business to investigate. It should be the police (or the taxman) doing it with them being allowed only to provide technical assistance when and where needed. Councils should be allowed to request a matter to be investigated and that is where their powers should end.
Unfortunately this is not the case - councils are allowed by UK law and precedent to pry into what is:
1. Various cases of fraud by misrepresentation - all the "who lives where and is entitled to what" cases.
2. Environmental issues of various sizes starting from minor misdemeanors like fly tipping to things that are criminal and have well defined crimes on the statute book.
3. Fraud of various shapes, colors and sizes related to the building trade and city planning.
4. Tax offenses of various shapes and sizes related to local taxation.
The pretext is that it will be "cheaper" than the police doing this. This pretext is false - each council uses hundreds of people across multiple departments where the police (and HMRC) would have used the part-time of less than 5-10 people to cover the same region. On top of that the councils _FAIL_ to bring most of the cases that should to be prosecuted to prosecution.
One you have fixed the underlying cause there will be no need for the council to look into anything. Until then, they will continue to ask.