Virgin Media and T-Mobile are the two mobile phone operators that offer unlimited everything (texts, data and minutes). Other operators like Vodafone, Orange, EE, Tesco Mobile, EE or Three offer unlimited minutes and texts or unlimited data but not all three. Furthermore, Three is the only one at the time of writing to offer unlimited data with tethering. T-Mobile is now part of Everything Everywhere while Virgin Media is a mobile virtual network operator and one of the biggest clients of EE.
Virgin Media' unlimited package is called the VIP SIM and costs £15 and is available both for traditional smartphone users and for BlackBerry users (offering unlimited email and messenger). Note that calls to 08 numbers are not included. As for T-Mobile, the offer available from Chitter Chatter on T-Mobile (full Monty) includes everything for £16. Note that both come with free Wi-Fi on the tube courtesy of Virgin Media.
There are numerous reports online pointing out to the fact that Virgin Media doesn't offer totally unlimited package with data being severely constrained. We would advise prospective customers to invest in a 30-day SIM only contract on both to check them out before making a commitment to either.