A plausible phishing scam is making the rounds, aimed at Apple customers, particularly those who have just received a gadget for Christmas.

The email purports to come from the company’s customer support, and asks for billing information to be updated. “Failure to update your records will result in account termination,” it says.

Unusually for such scams, the email is well-written and grammatical.

Customers are asked to click on a link which takes them to a sign-in page and then a page asking for credit card information. While the link looks genuine – store.apple.com – the related URL isn’t an Apple address.

“These well-crafted e-mails could fool many new Apple users, especially those who may have found an iPhone, iPod or iMac under their Christmas tree, and set up accounts with the iTunes Store or the Mac App Store for the first time,” says security firm Intego, adding that the scale of the attack is ‘vast’..

“We hope you’ll be careful if you’re new to Macs and Apple products.”

Facebook users, too, have been warned to be on the alert. They’re being offered the ability to give their profile a festive theme. The page leads to a malware that comes in the form of a browser plugin.

“Once users click the Like button, the page redirects them to a URL which allows victims to download and install a malicious plugin named Free Cheesecake Factory Coupons,” warns Trend Micro frauds analyst Nowelyn Ugsang. “Users need to be extra vigilant this holiday season.”