T-Mobile has become the first mobile-phone operator to offer a package that lets customers download software to make cheap or even free calls over the internet rather than its traditional network, potentially netting them big savings on their monthly bills.

The technology has already revolutionised home phones, with Skype’s “voice over internet” service boasting 100m users worldwide and household names such as Tesco getting in on the act, and it could do the same for mobiles.

T-Mobile’s move follows the launch of its “broadband internet” phone, the MDA Vario II, which promises internet speeds four times faster than current 3G handsets, allowing clearer transmission of voice over the internet.

By using the internet to make voice calls, customers can bypass the mobile-phone networks and the costs associated with them.

First you must sign up for a Vario II handset, priced at £39.99, on T-Mobile’s Flext 35 package, which costs £30 a month. For an additional £22.50 a month, you can now join T-Mobile’s Web ‘n’ Walk Max package, which allows you to download software, such as Skype Mobile, that routes calls over the internet. Calls to other Skype users, whether they are on landlines or mobiles anywhere in the world, are then free.

Calls to non-Skype users are also cheaper over the internet, especially if you regularly make international calls. They cost 1.4p a minute to landlines in the US, France and Australia, compared with 20p a minute to a UK line with a standard T-Mobile package and 70p to France. Skype calls to mobiles would be 16.6p compared with 20p on a standard tariff.

You get 900 free minutes of calls a month with the Flext 35 package, but only for UK calls, so people who travel regularly and make lots of international calls will benefit from the savings immediately.

Chris Frost of Uswitch, a comparison website, said: “The savings are considerable if a user makes international calls, especially to places such as the US, Australia and mainland Europe. However, you will start to save money on UK calls only when you exceed your free minutes.”

You would have to make at least 1,000 minutes of calls to UK landlines before you would start seeing any benefit, and a minimum of 5,000 minutes to mobiles, he said.

The disadvantage of voice over internet protocol (Voip) is that it only works in areas covered by T-Mobile’s internet network, which currently covers 70 per cent of the UK and is expected to hit 80 per cent next year. Cities are more extensively covered than rural areas.

On the other hand, the traditional network has near blanket coverage across Britain.

T-Mobile said it was previously reluctant to embrace Voip because of the poor quality of the calls resulting from slow mobile internet speeds. With the launch of mobile broadband, however, this has changed.

Speeds remain slower than home broadband, but the MDA Vario II will provide users with a connection at up to 1.8 megabits per second — up to 187 times faster than standard mobiles, which achieve rates of around 9.6 kilobits per second.