Studies like this have been examined before, and they always fall foul to three factors: confirmation bias, correlation != causation and poor statistics implementation.
It is, indeed, true that pockets of leukaemia are found around power lines. But, do you know what else is found around power lines... lots of families, including lots of children. There are less power lines in the country side passing near houses and less families with children in the countryside. So, it would be natural to see a small increase in childhood leukaemia around such power lines.
It's very similar to the one I saw in the Daily Mail recently, about asthma being more common around places with power lines within 100m... well, there's also a lot of smog in cities like that, so that's more likely to be the cause, rather than a bit of 50Hz (with limited power across a few more harmonics.)