Power lines give rise to electric and magnetic fields which fall off with distance. Burying power lines underground effectively shields the electric fields but less so the magnetic. And it is the latter that have given rise to most health concerns. Current exposure restrictions are based on limiting the electrical currents that time-varying magnetic fields induce in the human brain. Epidemiological studies have suggested that higher than normal exposure to magnetic fields could double the relative risk of contracting childhood leukaemia. However, a plausible biological mechanism has not been established. Overall, the evidence for a carcinogenic effect is still too weak to influence exposure restrictions recommended by the Health Protection Agency. These in turn follow the advice of the International Commission on Non-Ionizing Radiation Protection.
There are sometimes good aesthetic and practical reasons for replacing overhead power lines by underground ones. However, undergrounding power lines in response to health concerns would essentially be a precautionary measure.