Riband, I certainly didn't read the OPs post as an implication the locals start level at 2000ft. He simply said they ask for descent to 2000ft. You imply you were under radar vectors therefore I'd always ask for descent to an appropriate level for the approach we're shooting for.
In my experience, controllers, if vectoring me, may say 'Descend altitude 3500ft, Turn left leading 040, Cleared ILS approach RWY 01', and then after a few minutes 'Descend altitude 2000ft'. I would never consider descending below the initial restriction of 3500ft without further clearance unless I established on the localiser. Nobody I know in my company would take a 'Cleared Approach' clearance as a 'descend on discretion' while in 'No mans land' on radar vectors before they establish on part of the published approach profile - localiser, inbound course, etc.