The City Council, in addition to the taxes required by the general laws of the State, and required or permitted by the provisions of this charter, to be raised upon the property grand list and not included in the tax authorized by this section for City purposes may also annually at the same meeting and immediately after it gives final approval to the annual City budget, assess upon the property grand list for City purposes during the fiscal year, a tax which shall not exceed 52 and 76/100 cents upon the dollar thereof and may assess a larger tax when authorized to do so by the legal voters of said City at a meeting duly warned for that purpose.