There are currently 82 properties off supply.
A spokeswoman for Western Power Distribution said: "We received a call from a member of the public this morning about overhead lines down in the Chalford Hill area.
"For safety reasons we discharged the high voltage circuit, which affected 766 customers in the Chalford, France Lynch and Brownshill areas.
"When engineers arrived on the scene they were able to determine that the affected line was part of the low voltage network, so we were able to restore supplies to 684 customers after 21 minutes.
"We are now carrying out repairs to the overhead line so we can restore the remaining 82 customers.