This scam took in a perfectly savvy friend of mine, and I'd have fallen for it myself:
You get a phone call from the police. An authoritative-sounding man claims that your credit card details have been misappropriated. But the officer understands that you have to confirm his identity. So he provides his name and badge number and suggests you ring 999. Ask for the police, then quote the name and badge number, and you'll be routed to his extension.
His concern that in these perilous times you need to verify he's really a cop makes him seem authentic — and the process he recommends sounds foolproof. Yet as you follow his instructions, you may not realise that phone calls are only terminated by the caller, who in this case stays on the line — the better to play a recording of a dial tone (nice touch). When you ring 999, an accomplice ably mimics emergency services, then hands the phone back to the first man. Certain this is legit, you don't hesitate to provide your credit card details, and you're thankful when the "officer" offers to cancel the card for you.
Fortunately for my friend, she receives a text alert whenever her credit card is used, so when a £400 charge came in the next morning she rang 999 and asked for the police, objecting that Officer Whatshisface had promised to cancel the card. Of course, they'd never heard of Officer Whats-his-face, and had no idea what she was on about.