While most mobile operators have shunned Internet phone calling, British carrier 3 has launched a Skype-enabled phone that lets customers make free calls.

While other WiFi mobile phones let people download Skype software, none come with an out-of-the-box experience like 3’s Skypephone. The handset, which doubles as a conventional 3G cellular phone, has a dedicated Skype (EBAY) button and an address book that is integrated with the Skype service. That’s in contrast to many carriers who have steered clear of WiFi phones for fear Internet calling will cannibalize their revenues.

Kevin Russell, chief executive of 3’s United Kingdom operations, says he doesn’t share that concern.

“It’s been very clear for the last couple of years that we have to start embracing Internet communications,” says Russell. “We believe we can do that in a model that is very beneficial to 3.”

But 3’s “free Internet calling” machine isn’t completely free: The phone costs about $100 with a pay-as-you-go plan, which requires subscribers to buy monthly “top ups” (a.k.a. minutes that can be used for cellular calls or Internet browsing) at $20 a pop. Customers willing to sign up for a minimum 18-month, $25-a-month contract can get the phone for free. Currently, Skype Out — low cost dialing to regular phones — is not available and customers can only use Skype’s free service to call other Skypephones or people who have Skype software on their computers. The Skypephone features a 2-megapixel camera, Bluetooth and a 2-inch screen.

“It combines the essence of Skype with an advanced 3G phone,” says Eric Lagier, director of business development for mobile services for Skype, which is owned by eBay.

As the smallest and newest of carriers in the United Kingdom, 3 — a subsidary of Hutchison Whampoa — has little to lose by differentiating itself with the Skypephone. “We are looking to double our customer base,” says Russell.

The Skypephone will eventually be rolled out in additional markets, including Australia, Denmark, Macau and Italy. Customers in the United States will likely have to wait a while longer for the device — until the market “becomes more liberalized,” says Lagier.