The area of operation of a regional housing authority shall be increased from time to time to include one or more additional contiguous counties, except any portion thereof within a city until a resolution or resolutions are adopted by the council and the housing authority, if there be one, of such city, as provided in § 31-3-1010, not already within a regional housing authority if the legislative delegation of each of the counties then included in the area of operation of such regional housing authority, the commissioners of the authority and the legislative delegation of each such additional county or counties each adopt a resolution declaring that there is a need for the inclusion of such additional county or counties in the area of operation of such authority. Upon the adoption of such resolutions the county housing authority created for any such additional county shall cease to exist except for the purpose of winding up its affairs and executing a deed to the regional housing authority as herein provided.