The tree is due to be cut down to allow the building of a new sliproad onto the A303, as part of a £250 million project to turn the A road into a dual carriageway.
Activists have been living in the tree for two weeks and have described it as a "magnificent being". Protesters say they are willing to be arrested to save it from felling.
The exact age of the tree is disputed with protestors claiming it is around 600 years old while the National Highways say it dates back 400 to 450 years.
“The tree was not subject to a protection order and was deemed a veteran tree throughout the DCO (development consent order) process,” the National Highways has said
Indra Francesco, deputy mayor of Glastonbury and one of the activists at the site, has started a petition to save the tree.
She said: "A healthy veteran oak is threatened by National Highways to be felled for a slip road to a prep school as part of a road widening scheme on the 303.
"We object in the strongest terms to the removal of this tree, and request that plans might be adjusted to allow for its retention.
She suggested the slip road to the school be diverted "to allow a root protection zone for the tree."
"We have occupied the oak for the tree’s protection until National Highways and Gallifordtry Construction change the plans."
Speaking to ITV News on Tuesday, Ms Francesco said: "A tree that size would provide enough oxygen in a year for a family of five. There is also so much biodiversity which is reliant on the tree."
"There’s four of us currently in the tree. It’s going to take them a while to move us even with a specially-trained climbing team."
She said morale among the activists was "wonderful", and added: "When you are saving trees you are always in the right."
National Highways told the BBC that removing the tree was "a last resort" but moving the slip road would result in "severe delays".
"Where we plan to remove old trees on the A303 Sparkford scheme, we have made sure to investigate other possibilities to see if we can avoid removal. Sadly, that was not possible on this occasion," a spokesperson said.
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