The council is going ahead with a feasibility study to determine certain aspects of the possible arrangement.
They voted 9-3 at their most recent meeting last week to support a motion to ask Cumbria County Council for the first time to officially look into charging motorists who visit the national park.
The motion would provide a boost in health to Lake District's environment with the reduction of traffic, it would also provide new income which could be used to improve public transport services.
However councillor Steve Harwood, said:"I think it is totally wrong.
"We are lucky enough to be able to enjoy everything the national park has to offer and I think it is right that the opportunity should be available to everyone."