If, at or prior to final confirmation of any special assessment, more than 50% of the number of owners of privately owned real property to be assessed for any improvement, or in case of paving or similar improvements, the owners of more than 50% of the frontage to be assessed for any such improvement, shall object in writing to the proposed improvement, the improvement shall not be made by proceedings authorized by this Charter without a unanimous vote of all seven members of the City Council, provided that this section shall not apply to sidewalk construction.