The most recent consultation into the extension plans, which would cover Borrowdale and Shap, generated more than 3,000 responses.
Over 90% were in favour of the extensions.
The Campaign for National Parks President Ben Fogle says:
"The landscapes being considered by this Public Inquiry are the finest undesignated tracts of countryside in England.
"National Park status will not only help to protect the natural beauty and wildlife of these areas, but provide a much needed boost to the rural economy in these tough economic times."
A Public Inquiry has begun into plans to extend the boundaries of the Lake District and Yorkshire Dales National Parks.
It is expected to take around a month before sending recommendations to the Environment Secretary.
South Lakes MP Tim Farron has secured a debate in Parliament on whether to bring about direct elections to the boards of National Park authorities across the UK.
Mr Farron says it is essential for National Park boards to contain elected representatives so they are accountable for their decisions.
Mr Farron says that controversial decisions taken by the Lake District national park board over its Brockhole site on the banks of Lake Windermere have served as a reminder of this issue.
Commenting, Tim said:
The debate will take place on Wednesday 28th November in Westminster Hall.