The legislative body may provide by resolution or ordinance that no permit for the erection of any building shall be issued, unless a highway giving access to the proposed building existed and was established by law as a public highway at the time of the establishment of the official map in accordance with this part; provided, that the resolution or ordinance shall contain a provision whereby the applicant for the permit may appeal to the board of adjustment provided for in §54-18-212, hearing upon the appeal and notice of which shall be held and given as provided in this part, and the board shall have the authority to authorize a permit, subject to conditions the board may impose, where the circumstances of the case do not require the proposed building to be related to existing streets or to streets shown on the official map, and where the permit would not tend to distort or increase the difficulty of carrying out the official map or master plan of the county or municipality.