Since the usage of cellphone has risen in the past 20 years with noticeable amount (you bet) the researchers suggested that from the data they analyzed from UK Office of National Statistics from 1998 to 2007 would show a noticeable uptick in the data. But according to them it is not.
According to researchers, it is assumed that around 5-10 years of high exposure is necessary for brain cancer to arise. So logically the 1998-2007 is pretty long. Here is a quote from their research paper concerning the matter...
Our analysis suggest that the increased and widespread use of mobile phones, which in some studies was associated to increased brain cancer risk, has not led to a noticeable increase in the incidence of brain cancer in England between 1998 and 2007. Therefore, it is very unlikely we are "at the forefront of a cancer epidemic" related to mobile phone use. A small increased rate of brain cancers in the temporal lobe was observed corresponding to the time period when mobile phone use increased from 0 to 65% of households. However, to put this into perspective: if this specific rise in tumour incidence was caused by mobile phone use this would contribute to less than 1 new case per 100,000 population in a decade. We cannot exclude the possibility that there are persons who are susceptible or some rare brain cancers are associated with to RF from mobile phones. However, we interpret the present data as not indicating a pressing need to implement the precautionary principle to reduce exposure to RF from mobile phones by means of population-wide interventions.
Source : this Washingtonpost cellphone and cancer risk article.