How far can people like DWP snoop on you?

Yes they can and they can also check your medical records without your permission.

Jesus Antono is asking because it's reasonable to assume you're worried that the government is going to find assets that you don't want them to find. Otherwise, there's not much of a reason for you to ask this question.

But yes, you typically sign a waiver when you apply for benefits that allows them access to your financial statements like bank account balances. They can't just go into your email or FB without a court order though. HOwever, if they have evidence you're trying to hide assets to gain benefits, they could get it.

To access your FB account they need a court order (which they can get fairly easily). When you apply for benefit the statement you sign basically gives them your permission to go through your financial accounts, liaise with Local Authorites, credit reference agencies, etc.

It is a crime to defraud in this manner, so they do have the power.

Yes. Fraud investigation has no boundaries. Rightly so of course.

As long as they comply with RIPA requirements