Residents living next to the former Rangers manager's Colinton mansion say the trees which line the estate – estimated to be 60ft high in some parts – are ruining their quality of life by blocking out sunlight from their properties and gardens.
And they insist that despite asking the property's current owner to cut them back for nearly three years, little has been done.
Aileen Maclean, 62, has lived in her house on Laverock Dale Park with her husband Andrew, 65, from around 27 years.
The property is adjacent to the north side of the mansion, on Dreghorn Loan, separated by leylandii trees which she believes are now an average of 30ft high, having not been cut for around ten years.
She said: "The trees were planted by Graeme Souness when he built the house. He was always very civil and said that when they reached what we all agreed was an acceptable height, he would make sure they were cut back. But, of course, he eventually moved on.
"Our garden is now very dark, we have to have lights on in our kitchen all day and although we used to be able to see the Pentland Hills from our house, we cannot now."
The mansion, where former Scotland international Maurice Johnston also stayed for a brief spell, has changed hands twice since Souness' departure.
Its current owner, who bought the property three years ago, has been developing it for re-sale and has not been living on the site.
There are seven houses along the boundary of the mansion and residents say they have joined together to repeatedly try to get the owners to cut the trees to what they believe is an acceptable height. But they insist that despite asking for action they have had no luck and some of the trees are now around 60ft high.
Resident Alan Haxton, 69, whose property also backs on to the mansion, said: "In my opinion there has been a great degree of selfishness.
"We cannot use our garden as we would like to and we cannot grow things in it as we would like to either."
The residents are now using the support of campaign group ScotHedge which fights for residents' rights.
Their campaign coincides with a public consultation led by the Scottish Government, attempting to measure the scale of such issues and seek views on how disputes could be effectively resolved.
Rory Milne, a partner with Archibald, Campbell and Harley, based in Edinburgh, is the solicitor for the current owners of the mansion.
He said a bereavement in the family prevented them from moving into the property, which is due to go on sale next week.
But he insisted the trees had been cut last spring to a height deemed acceptable by neighbours, except for a small corner which could not be accessed at the time.
He said: "There is only the corner section left and that is going to be dealt with.
"I do not think there was a dispute – we did what we were asked to do."