BT has urged broadband customers to be vigilant for potential scammers.
A correspondent called RG contacted the Telegraph to say his wife had received an email purporting to be from Openreach.
When opened, it displayed a letter from BT, along with a logo saying "New BT Online Notification", followed by a "hello" and the recipient's email address.
The letter said: "Your monthly payment was recently declined. The decline could be due to insufficient funds, card expired, etc.
"Since you haven’t provided us new billing information yet, we thought we’d remind you to please provide us with updated billing information to avoid any billing problems with your account. Thanks for choosing BT."
The Telegraph described this as a "classic phishing email" and said the email actually contained some clues that it was not a genuine communication.
For instance, the newspaper noted that it is BT rather than Openreach that bills broadband customers.
BT confirmed that the scam became operational on the day the email was sent and said it took steps to close down the fake website linked to from the message within 12 hours.
The company has advised customers to make sure they never share their BT account number with anybody and to always shred their bills.
"Be wary of calls or emails you’re not expecting," BT added.
"Even if someone quotes your BT account number, you shouldn’t trust them with your personal information."