Guarantees are being sought from the government over the level of support for Cumbria when the Sellafield nuclear plant closes.
About 12,000 people currently work at Sellafield
A predicted 8,000 jobs will go as the reprocessing plant is decommissioned over the next 10 years.
Cumbria County Council is lobbying the House of Lords, which is debating the Energy Bill.
The council has written to peers seeking guarantees of financial and social support for Cumbria.
In a joint move, the council's three political group leaders have written to peers from each of their political parties seeking support.
A spokesman for Cumbria County Council said: "We have welcomed the fact that the new Nuclear Decommissioning Authority (NDA) will locate its headquarters in west Cumbria.
"The exact location is still being considered.
"As things stand, the NDA only has a power to give encouragement and other support activities benefiting the social and economic life of communities living near nuclear sites.
"The council believes this is not strong enough and is lobbying for the NDA to be required to do so and not simply leave it to the authority's discretion."
The council's three political group leaders: Tory, Rex Toft; Labour's Stewart Young, and Mike Ash of the Liberal Democrats, issued a joint statement.
It said: "We have welcomed the setting up of the NDA to manage the decommissioning of nuclear sites across the country and the fact that its headquarters will be in west Cumbria.
"But it is essential we get guarantees that social and economic support will be given to those areas hit by job losses."
In December 2003, the government announced a taskforce to ensure the economic future of west Cumbria.
The new taskforce, which will have more than £100m available to spend over the next five years, will be responsible for developing a new social, educational and economic infrastructure for the area.