Crossing the FAF without approach clearance
Was giving dual instruction in VFR (not on an IFR flight plan) the other day to an instrument student (Miami area). Was on with approach and requested an ILS approach. We got vectored and intercepted but never received 'cleared for XYZ ILS' from the approach controller. We got to glide slope intercept and my student asked if we could continue, knowing we hadn't received the clearance. The class D was quickly approaching so I told my student to end the approach and proceed out and away from the class D. Then I advised ATC we broke off from the approach and were going to squawk 1200. Now I realize it's a VFR flight, and that just simply asking ATC if we were "cleared" was the right thing to do. The issue was how busy he was at the time I could not call to verify, which led me to breaking off.
What is the proper procedure here? Contact the class D's tower and do the approach anyways because we are VFR? What about if it had been under IFR? Ultimately I am curious if, under IFR, you do not receive the approach clearance but you cross the FAF what is the correct course of action? Execute a missed approach?