My elderly neighbour was almost taken in recently by a scam claiming to be from the council - the story was that nationwide council tax bands are being reassessed and she was on a list that could be back-dated 20 years and she would be able to claim £4,000 back. They offered to fast-track it for a payment of £100. By chance, she had been talking to the council about something else recently and this made it all seem more genuine. Thankfully she had enough doubt to ask me first - but was then doubting me when I told her it must be a scam. We put it to bed after I Googled the phone number they called from, which had a long list of complaints registered against it.
It's easy to see how people are taken in sometimes when the call or email gets the right bank or happens to resonate with your circumstances in some other way.