Enfield Council says it has carried out extensive works over the years to protect the historic Oak, but even more needed to be done. Councillor Chris Bond, said:
"Our primary objective is to save this fantastic natural monument which predates the Magna Carta. Doing nothing is not an option, because unless we take decisive action, this historic and much loved tree will fall over.
"If that were to happen the it would cause extensive damage to the park and potentially damage nearby homes. "The action we are proposing, while drastic, gives the tree a good chance of recovery and means that future generations can enjoy it for years to come."
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A lamp in the tower which houses Big Ben is to be switched off for the first time in more than 70 years.
Sir Bruce entertained audiences for more than seven decades.
Work in the tower will also pause over the bank holiday weekend.