Either the occupier or owner can open the letter.
Unless you live in a multiple-occupancy building where the Valuation Agency has used an 'aggregation' policy for determining the Council Tax band for the property as a whole (which is quite rare) it is your responsibility, as the tenant, to pay Council Tax, not that of your landlord.
Chris
PS: Most people wouldn't be as fussy as you about opening letters. If something drops through my door, I open it and read it. If it turns out that it should, for example, have been delivered to a neighbour, I simply put it through their letterbox with "Sorry, opened in error" written on it ;-)