Gardeners have been tending to the 30ft plants for the past three days.
Angry residents have said it has bought "chaos" to the area, as four way traffic lights have caused major tailbacks on the surrounding roads.
"The hedges are obviously to stop people looking into her property," one neighbour said. "It's just taking ages for them to cut the bush back. The gardeners have been here three days and have finished the front of the garden.
"It's chaos around there. The lights are taking too long to change, especially on the side roads. There is long queues tailing back from the lights."
The Leyland cypress is widely used as a quick-growing hedge or screen, and can to grow as high as 50ft if left untended.
According to the Royal Horticultural Society's (RHS) advice page on 'Leylandii' or Leyland cypress, the plant has been viewed as a "neighbourhood nuisance".
"With little or no pruning, it can quickly grow to giant proportions and overshadow gardens," the RHS advise gardeners.
"It is widely used as a quick-growing and effective hedge or screen. However, if left un-pruned it can get out of hand and pruning taller hedges can be difficult and expensive."
Neighbourhood dispute
This is not the first time Rowling has courted controversy among her neighbours.
In 2011, the multi-millionaire author was granted planning permission to knock down a £1million 1970s style house she bought next door to her own home to allow her to enlarge the garden.
The announcement caused a stir, with one local resident commenting: "It is not everyday you hear someone seeking approval from their neighbours to flatten a £1million house to make their garden bigger."
The following year she won planning permission to build two luxurious Hogwarts-style tree houses in her garden, despite protests from local residents.
The writer applied to have the 40ft high structures erected, at an estimated cost of £250,000, as part of a programme of major renovations at her home in Edinburgh.
The two-storey structures on stilts feature secret tunnels, a rope bridge and turreted roofs.
At the time, residents living nearby lodged objections with Edinburgh City Council, claiming the size of the tree houses meant they would be seen from the road and would blight the conservation area.
Dr Patricia Eason, secretary of the Cramond and Barnton community council, said the tree house development was "unacceptable" and "quite out of character with the area".
Ms Rowling's neighbour Tom Borthwick, 66, had also raised concerns about the size and safety of the tree houses and sought assurances they could not be viewed from outside the property.
The author bought her 17th century mansion for just over £2million, five and a half years ago. She lives there with her husband Dr Neil Murray, their two young children and her 19 year old daughter, Jessica, from her first marriage.
Ms Rowling declined to comment.
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