This is almost certainly a con.
To check try logging in to the bank site as normal (not using the link given in the email). If you can access the site as normal then the email was not from your bank.
If on the other hand you cannot access the site then contact the bank in person and ask if they did send the email.
Banks will never request your details as they already have them, and as they do not want any data lost (it could cost them millions) they are very careful about keeping backups.