The Labour politician, now Baron McConnell of Glenscorrodale, is fighting a civil case with his wife, Bridget, against Norma Hunter, 69.
The couple argue that the 3ft-square shed – on the boundary of their garden and Mrs Hunter’s in Victoria Place, Kings Park, Stirling – is their property.
But Sheriff Wyllie Robertson yesterday threw out an application for an interim interdict from their lawyer, Ian Smart, that would have banned Mrs Hunter from using the building, where she keeps mops and tools, until the case is resolved.
Sheriff Robertson said: “Let’s be real about this. This is a motion for interim interdict. If the defender continues to use the cellar in breach of interdict the defender could be sent to prison.”
Stirling Sheriff Court heard that the McConnells have a ground-floor flat, with retired Kirk minister the Rev Malcolm MacRae, 66, their neighbour in the basement, while Mrs Hunter owns the house next door.
The cellar sits on its own at the back of the couple’s property and can currently be accessed by Mrs Hunter, the McConnells and Mr MacRae, but the clergyman is laying no claim to the cellar.
Mr Smart argued that the cellar was part of the staircase which was joined on to the basement of the McConnells’ property, so should be theirs.
However, Anthony Quinn, for Mrs Hunter, said: “The cellar is distinct from the internal staircase and distinct from their property.”
Mr Smart argued that Mrs Hunter, who has lived in the street for more than 20 years, should not be using the cellar. He said the McConnells had a land certificate which shows they have “title” to the cellar.
However, the court was told that there were errors in the certificate.
Throwing out the interim interdict, Sheriff Robertson said: “The real difficulty I have is the remedies for breach of interim interdict are penal.”
He granted a defence motion that the McConnells should pay Mrs Hunter’s expenses for the decree motion, along with that for interim interdict.
An options hearing was set down for 14 days’ time.
Mr MacRae said after the hearing yesterday he believed the shed belonged to Mrs Hunter, rather than the McConnells. He said: “My solicitor investigated ownership of the cellar, but, according to plans, it belongs to Mrs Hunter. I have no doubt it belongs to her, and have stepped back from it since then.
“I’ve tried to help as a peacemaker, but to no avail. Mrs Hunter has currently got the door to the cellar chained up. Hopefully, they will get it resolved soon.”
Neither of the McConnells were at home, and neighbours said they are often away on business.
Lord McConnell, 51, the former leader of Stirling District Council, was Scotland’s First Minister from 2001-7, making him the longest-serving First Minister in the history of the Scottish Parliament.
He was MSP for Motherwell and Wishaw from 1999 until last year, and was made a Labour peer in 2010.
He talked last year about his joy at moving to his new home in Stirling, and how well he was getting on with his neighbours and locals.