What are you basing your claim of increased cancer on? As an outsider, the only way I can get a grip on the situation is to look at claims, and the support for those claims.
for an outsider google is your friend (i intentionally didn't mention any specific cases i'm personally aware of because they can be easily shot down by "sample of 1" type of argument even though everybody around understands what it really is). For example:
"After the Chernobyl accident, children from Belarus living in highly exposed regions received mean thyroid doses by radioactive fallout higher by a factor of approximately 2 as compared to the survivors of the atomic bomb explosions. This lead to a radiation related increase of thyroid cancer incidence in children and adolescents with the highest incidence in age group 0-4 years up to now totally amounting to approximately 5 000 cases. "
Among the residents of Belarus, the Russian Federation and Ukraine, there had been up to the year 2005 more than 6,000 cases of thyroid cancer reported in children and adolescents who were exposed at the time of the accident, and more cases can be expected during the next decades. Notwithstanding the influence of enhanced screening regimes, many of those cancers were most likely caused by radiation exposures shortly after the accident. Apart from this increase, there is no evidence of a major public health impact attributable to radiation exposure two decades after the accident. There is no scientific evidence of increases in overall cancer incidence or mortality rates or in rates of non-malignant disorders that could be related to radiation exposure. The incidence of leukaemia in the general population, one of the main concerns owing to the shorter time expected between exposure and its occurrence compared with solid cancers, does not appear to be elevated. Although those most highly exposed individuals are at an increased risk of radiation-associated effects, the great majority of the population is not likely to experience serious health consequences as a result of radiation from the Chernobyl accident. Many other health problems have been noted in the populations that are not related to radiation exposure.
>There is no scientific evidence of increases in overall cancer incidence or mortality rates or in rates of non-malignant disorders that could be related to radiation exposure.
for each cancer you can google and find things like this:
"In addition, a significant two-fold increase in risk was observed, during the period 1997-2001, in the most contaminated districts (average cumulative dose of 40.0 mSv or more) compared to the least contaminated districts"
>more cases can be expected during the next decades.
yes. We're about in the middle right now - following known models of radiation exposure health effects the total numbers are projected to double over the next 20-30 years.
http://www.ncbi.nlm.nih.gov/pubmed/18923372
"After the Chernobyl accident, children from Belarus living in highly exposed regions received mean thyroid doses by radioactive fallout higher by a factor of approximately 2 as compared to the survivors of the atomic bomb explosions. This lead to a radiation related increase of thyroid cancer incidence in children and adolescents with the highest incidence in age group 0-4 years up to now totally amounting to approximately 5 000 cases. "