It is quite normal for your the 3rd party solicitor to file claimant NI details as part of closing a file due to the potential claim from the government for repayment of benefit recovered in the settlement of a claim. It sounds like this is not the case in your wifes case but the lawyer will request the information as a matter of course.
they will not require the bank details as compensation is normally paid by cheque direct from the defendants solicitor or insurance company.
If you have any niggling doubt, ask the agent why they require this information before suppying the same and if you can find no valid reason for the request, don't pass it over.
It is highly unlikely that there is a scam going on here as they would require much more information to do you any harm.
Mark
compensation uk