The former RBS boss has been feuding with neighbours for more than four years over his double-layer, 25ft leylandii hedge that shields the £3.5 million property in the upmarket Colinton area of the city.
A new law is due to come into force in April empowering local authorities to make and enforce decisions in relation to high hedges disputes. But some neighbours decided not to wait, and chopped down a layer of leylandii in a bid to let light into their gardens.
One resident, who asked not to be named, said: "Some of the residents have taken matters in their own hands and just cut them down.
"I think they just took a chainsaw to the hedge and did it themselves. They just got fed up of waiting for a decision to be made.
"The first row of leylandii is directly connected to the fences of the residents' houses, and that is the ones that have been cut.
"Ideally they want to cut the hedge down to the same height of their own fences, so to just a few yards high. It doesn't look very nice as you can now see all the dead leylandii that has not been able to grow due to no sunlight. That needs to get cut down as well."
The former RBS chief executive bought the six-bedroom home, built by football legend Graeme Souness, in June 2011 after his property in The Grange was targeted by vandals.
After he split from his wife Joyce she remained at the new address, and although recent efforts have been made to reduce the size of the hedge, neighbours still believe it is unacceptably high.
Another resident said: "She should just pay to have it cut down. We will try and talk with her before we begin arbitration. We should be able to enter one together as residents and split the cost.
"Why we, the innocent party, have to pay I don't know, but we will as this dispute needs to be settled."
Together they plan to become one of the first groups in Scotland to take action under the new High Hedges (Scotland) Bill.
It gives councils the right to force homeowners to cut hedges that are more than 6ft 6in tall if they form a barrier to light.
Councils have the power to enforce cutting back orders if owners do not have the work carried out themselves.
The council can then charge up to £500 to carry out the pruning if the homeowner does not complete it at their own expense.
Joyce Goodwin, speaking on an intercom at the Colinton house, said "What hedge?" when asked for comment. She then hung up.