Any person aggrieved by the refusal of the Mayor to grant any permit required under the provisions of this article may appeal the decision of the Mayor to Council. Such appeal shall be prepared in writing stating why the appellant is aggrieved, with the reasons therefor, and shall be filed with the Town Clerk within ten days from the date of the refusal of the Mayor of any such permit. Council shall hold a public hearing upon such appeal at its next regular meeting after the filing of the same, and shall render a decision upon such appeal without undue delay.