Before the legislative body may proceed after the preliminary confirmation or finally confirm the proceedings, including the diagram, assessment, and proposals, there shall be filed with the clerk written consents to the assessment readjustment and bond refunding proceedings as preliminarily confirmed and to the readjustment of the assessments and the refunding of the bonds pursuant to such proceedings. The consent shall be signed by the owners of a majority in area of the lands in:
(a) Each district whose bonds are to be acquired.
(b) The new district.