Derek Hollingworth
The Donisthorpe factory, in Bath Lane, is believed to have been one of the first ever factories in Leicester, as well as being the oldest surviving one.
It opened in the 1790s as a stubbing mill – where sheep fleeces would be combed by hand to prepare them for spinning into wool.
Its construction came shortly after the work was completed to make the River Soar fit for boat travel between Leicester and Loughborough.
The building, also known as Friars Mill, is near to the new Highcross car park, on land earmarked for development.
Two years ago, the factory was hit by lead thieves who took the metal off the roof.
The hole was covered with tarpaulin but the material is now in shreds, prompting Leicester City Council to contact the owners, Urban Invest, about securing the building.
The Leicester Civic Society and Leicester Industrial History Society have jointly petitioned English Heritage to get the building extra legal protection by upgrading its listed status from Grade II to Grade II*. Two months ago, the site was broken into again and the gold-painted ibex figure – the brand of the Donisthorpe hosiery company – was taken from the roof.
Civic society deputy chairman Derek Hollingworth said: "The fate of this factory is a top concern for us.
"The tarpaulin on the roof is in tatters and when water gets in the wet rot starts to damage the timber structure.
"Then you get dry rot and before long the wood just turns to dust. Something needs to be done."
Urban Invest has planning permission to build a 23-storey apartment building near to the factory, along with a four-star hotel. The £60m scheme – which was unveiled in March 2008 – would involve using the factory, possibly as a restaurant.
Mr Hollingworth said he understood that the development was on hold because of the recesion. He said the civic society hoped the Council would be able to cover the roof.
A spokesman for council said: "We are discussing repair options with the owners of the building. The council does not intend to allow the building to fall into disrepair."
Urban Invest, which gives its address as being in the British Virgin Islands in the Caribbean, could not be contacted.