This is a fascinating question that never seems to go away.
First, to answer captp's original question - and I offer my input for a UK controller's perspective - I would not expect a pilot to descend below the last level that I had assigned until established on the LLZ (and, for the really pedantic amongst us, given a clearance to descend on the ILS). But I would be alert to the possibility that a pilot might descend simply because of the differences of opinion being expresed in this thread.
It has happened to me on a handful of occasions over 20-odd years of controlling - sometimes it matters, and I've had to do something to ensure separation from other traffic, other times there has been no traffic problem and my only concrnn has been that the aircraft does not descend below terrain safe level. It's not an ideal situation but I recognise that I'm not going to change it so I try to find ways to live with it in the best way possible - so I won't bother getting into the debate about who uses the 'right' phraseology! Except to say that unless pilots have a consistent understanding of the meaning of a standard phrase, standard phraseology offers few benefits.
On a more general point, I think the question that captp asks highlights a distinction that is probably clear to controllers but seems to be blurred in pilots' minds. If an aircraft is under radar control and I'm giving vectors, I am responsible for assigning levels that are terrain safe and for pointing the aircraft in the direction it should go (accepting, of course, that the pilot-in-command is always ultimately responsible for ensuring the safety of the aircraft). This is why, when vectoring to the ILS, I expect the aircraft to fly at the levels that I specify - which will include a clearance to descend on the ILS when it is appropriate given the traffic situation.
If I am controlling without the benefiit of radar, the pilot is responsible for remaining terrain safe. I will give a clearance that is valid at the relevant fix - safe from other traffic all the way that the clearance covers and terrain safe at the fix - how the pilot gets to the fix, subject to any restrictions that are included in the clearance, is up to him or her. In this circumstance, when I clear the aircraft for the ILS procedure, I expect the pilot to follow the procedure track and to assur that the aircraft remains terrain safe. The approach procedue will define minimum levels to be flown at various points in the approach and I understand that the pilot may choose to desend to the specified level immediately or, alternatively, may elect to manage the descent profile to give a continuous descent where this is possible.
As a controller, the distinction between the two types of ATC service - and the procedures that pilots should follow - is very clear but perhaps this is not the case from the pilot's seat.