The Charity Children with Cancer ran a three-day conference in London 5-7 September 2016, and linked to that conference, there were stories in the media about the increase in incidence rates for cancer in children, teenagers and young adults, and what might be causing these increases.
see e.g. the Sunday Telegraph.
Power lines were one of the possible factors mentioned.
The Childhood Cancer and Leukaemia Group then published a response.
There seems to be agreement that childhood cancer rates probably are going up, though uncertainty as to how much of that is simply better diagnosis. There are very few definitely known causes, but various suggested or possible causes, with varying strengths of evidence. One of those possible causes is magnetic fields, from high-voltage power lines or other uses of electricity, or perhaps some other factor associated with the power lines other than magnetic fields. This site is devoted to presenting the evidence on this subject. But, specifically on the trends over time, this has been looked at in some detail. Although exposures to magnetic fields and childhood leukaemia rates have both increased, the big increases in each were at different times (exposures had their biggest increase after the second war, leukaemia rates before), so this does not really provide any evidence in support of a causal link.
See more detail on:
the evidence on childhood leukaemia generally