There are calls for neither Sellafield nor Chapelcross to be chosen to store radioactive waste from dismantled nuclear submarines.
They come after the Ministry of Defence included the two facilities on a shortlist of potential sites for the project.
But both local authorities have formally objected to the idea, saying it won't benefit their area.
1,300 contractors have walked-out at Sellafield for the second time this week.
They originally downed tools on Monday after a dispute over scaffolding on a project to replace old ventilation.
While the issues surrounding that have been resolved, the workers are now unhappy with contractor Doosan Babcock and several health and safety Issues.They have said they plan to remain on strike until Monday.
Doosan Babcock hasn't commented.
Contractors that walked-out at Sellafield on Tuesday have returned to work today.
Talks to settle the dispute are also set to start as part of the agreement to workers ending the "unofficial action".
The mass walk-out was caused by a disagreement between two companies over who owns a piece of scaffolding at the site.
The mass walk-out at Sellafield has reportedly been caused by a dispute between two companies over who owns a piece of scaffolding at the site.
The union UNITE is claiming its members may not be insured to touch the equipment.
The main contractor Doosan Babcock has said it's in talks with unions to try and resolve the matter.
"Doosan Babcock can confirm that it is in consultation with its employee union representatives to fully understand and resolve the unofficial industrial strike action undertaken at Sellafield.
"While those talks are underway, we are unable to comment further."
Around 1,300 contractors based at Sellafield have walked out over a dispute between a main contractor and a sub-contractor.
Those striking work for a number of sub-contracting firms that operate under the umbrella of the National Agreement for Engineering and Construction Industry and were reportedly working on building projects.
Sellafield Ltd has responded to the "unofficial action", stating that the dispute does not directly involve the company.
"Sellafield Ltd is not directly involved in the dispute, which does not involve any of our employees, but we have taken steps to ensure that safety and security at the site are unaffected by this unofficial action, and we will be closely monitoring further developments.
"This unofficial action is as a result of a dispute between a main contractor and a sub-contractor"
Around 1,300 contractors based at Sellafield have walked out.
Workers downed tools at midday and are not expected to return to the site until Wednesday.
The industrial action is the result of a dispute between a main contracting firm and a sub-contracting firm on the nuclear plant where more than 10,000 workers are based.
Controversial plans for a budget hotel in the centre of Penrith have been approved by Eden planners.
A Premier Inn will be built in the New Squares area of the town, despite some bed and breakfast owners opposing the idea.
But Planners said they were likely to turn down an application for a petrol station, close to the new hotel. The final decision is will be made at a later meeting.
Yesterday the final piece of track in the Borders Railway was laid by Transport Minister Keith Brown.
Jenny Longden reports.
Scotland's Transport Minister says the new Borders Railway will put the area on the map:
The £350 million Borders Railway has been completed with the final section of track laid this morning.
Scottish cabinet secretary for infrastructure, investment and cities Keith Brown arrived at Tweedbank Station by train before clipping the final piece of track into place.
Work to lay the track began in October and the line will open to passengers between Edinburgh and the Borders on September 6 2015.