The CCRG study published its original results in 2005, which found that childhood leukaemia rates were elevated within 600 m or the highest voltage power lines in the UK.  It then published an update in 2014.  This found that the effect - the elevated leukaemia rates - were highest in the 1960s then declined over the subsequent decades, a frankly puzzling finding!  This is the main results graph from the 2014 paper:

But that latter paper analysed the leukaeia rates in quite broad bands - 0-200 m and 200-600 m.  In 2018, CCRG published a Note, which looked at the rates in finer bands.  This found that when you look at these finer bands, you no longer get a pattern of the highest rates closest to the line. Instead, the rates are highest just a bit out from the line, about 100 or 200 m out. They decline further out, but they are also lower at the very closest distances.  This is the results for 275 and 400 kV lines:

Neither the authors nor anyone else knows what this really means.  But it's probably fair to say it is the final nail in the coffin of any idea that this is a direct physical effect of the power lines.  It seems more likely that whatever is going on is something indirect, perhaps an effect of how population characteristics vary with distance.  The authors themselves speculate about whether it could be linked to residential mobility - how often people move house - although they are pretty cautious (they actually say that this looks like "the least implausible" candidate explanation).

see more on residential mobility and related theories