The Robinia – or false acacia – is located on Westminster Bridge Road, just inside the hospital grounds on the approach to Westminster Bridge.
In their application to Lambeth Council, tree consultants to Guy's and St Thomas' NHS Foundation Trust say that "this tree is over mature and in advanced decline with major deadwood evident throughout the upper crown.
"Crown reduction pruning is not considered appropriate as it would render the tree unsightly in such a prominent location."
The tree is subject to a tree protection order so permission from Lambeth Council is being sought under application 21/03843/TPO.
In a flurry of tree-related applications to Lambeth planners, Southbank Centre is planning to reduce or reshape 36 of the London plane trees along the Queen's Walk that fall within its ownership (21/03874/TPO).
The description of works includes "clearance pruning around lamp columns for increased visibility and safety at night".