The FSCS has confirmed that it does not approach people in this manner and had advised consumers not to respond to the emails or provide any information.
The scammers attach a fake form asking people to give personal information and send a fake identity card which they claim is from an FSCS staff member.
The compensation scheme has recommended that anyone who receives such an email delete it immediately and block the sender using their email security settings.
FSCS chief executive, Mark Neale, said: “Sadly, such scams are one of the plagues of modern life. They prey on people and try to lure them into handing over their personal information on the promise of riches. Don’t let scammers get away with this.
“The FSCS will never approach you in this way. Stay safe. Do not respond to these emails or provide any personal information.”