It will be the second attempt by applicant Philippa Howcroft to remedy the impact the tree has had.
In 2013, the council dismissed her bid to prune the tree after it decided the application did not contain enough detail on which to make a decision.
This time she is seeking to remove the tree at the end of a row of three protected London plane trees. Her application has been supported by 28 residents living in close vicinity to the trees, and opposed by eight residents.
Anthony and Gillian Cotton said the trees had never been pruned and risked damaging houses in storms. Roofs and gutters needed to be constantly cleaned and they lost the evening sun at an early hour. The Cottons said all three trees should be removed because they had no aesthetic value.
An opponent of the application, Sonia Forlong, said the removal was for financial gain and that living next to the plane tree was the choice of residents. Removal of one tree would not alleviate leaf fall as there were two other trees, and she would be more supportive of pruning.
Opposition from further afield included concerns that removing one tree would lead to the rest being felled and affect the visual panorama.
Council environmental planner Kahurangi Tapsell has recommended refusing the application. He acknowledged the tree would shade a future development, create maintenance problems from leaf and debris fall, and reduce the flexibility of the building's design.
However, he said no other options were put forward by the applicant, whether by pruning or designing the house within the drip line of the tree.
Mr Tapsell said the crown of the tree extended about seven metres into the vacant section and aerial photos showed the three trees were well established in 1977 - many years before the area was subdivided.
He argued that the reasons to remove the tree had to be balanced against the need to maintain urban character, a key part of which were notable trees. "I do not believe that the reasons put forward by the applicant were sufficient to warrant the tree's removal."
A report from Richard Coles of Boffa Miskell, representing the applicant, said the house-maintenance issues had put off potential buyers.