South Lakeland District Council is considering a legal challenge against a decision which could wipe it off the local government map.
As well as being asked about regional government the people of the North West will be asked to choose the kind of local councils they want.
Options include a single council for Cumbria; or a two-way split between a new Morecambe Bay authority comprising South Lakeland, Barrow and Lancaster and a single North Cumbria authority.
A joint statement from South Lakeland, Eden, Carlisle, Allerdale and Copeland councils, said: "We are extremely disappointed. We are seeking, as a matter of urgency, a meeting with the Deputy Prime Minister."
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