There still aren't any good explanations for how mobile phones could cause cancer. The radiofrequency electromagnetic radiation they transmit and receive is very weak. This radiation does not have enough energy to damage DNA, and cannot directly cause cancer.
In 2012 an independent report concluded that there is no convincing evidence that being exposed to radiofrequency fields, including those from mobile phones, within the guidelines could affect somebody's health.
The UK follows a set of international safety standards, which restrict the amount of electromagnetic radiation people can be exposed to and have a very large safety margin.