Electricity North West tweeted a photo of the man on Saturday, saying he escaped with only “a tingle” after trying to move the branch, which Storm Emma had brought down over a power line.
The man phoned Electricity North West, which then cut the power from the 11,000-volt line in Mottram, Hyde, in Greater Manchester.
“This has to be the luckiest man alive,” said Chris Fox, incident manager for Electricity North West.
“Electricity can travel through things like branches and can kill instantly. It can also jump, so how he avoided death is simply incredible.”
The network operator has been battling Storm Emma in restoring power to 23,000 homes as wind and fallen trees have damaged overhead lines.
“He owes his life to a freak combination of circumstances which we still can’t quite fathom, including his gloves, his strong walking boots and the fact the branch must have been completely dry.
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“Even so, we can’t believe he escaped unharmed. As soon as he contacted us we cut power to the line, and our specially-trained engineers and linesmen have attended site to remove the branch.
“It is essential for anyone who sees lines down or debris touching lines to stay away and call the emergency power safety number 105 as soon as possible. This will put them straight through to their local network operator who can deal with the situation safely.”