Electric Field Energy Harvesting (EFEH) systems use the high voltage power lines of an electrical grid to provide power for the low cost distributed electronic measurement systems that are needed to monitor these lines for Smart Grid operation. However, the challenge with EFEH is to extract useful amounts of energy while avoiding close proximity to (or even galvanic contact with) the power line. The primary constraint is the weak parasitic capacitive coupling that interfaces between the power line and the power supply system, which severely limits the amount of continuous power that can be extracted. This paper addresses this challenge, by rectifying the weakly coupled AC into a high voltage DC source, and then using a flyback converter operating in discontinuous mode to transform this voltage down to levels that are useful for electronic systems. The investigation has identified that up to 17 mW of continuous power from a 12.7kV MV line can be extracted using this approach. Matching simulation and experimental results are presented in the paper to validate this performance