2000' is NOT the "start level" - there is no such thing.
Got the shout from your caps...
CDA into LHR - Cleared 3000', aren't we always on the glide well before that?
CDA into DXB - Any different? But procedurally what did the ATCO do wrong apart from the clearance being a little reversed? If they had said 'Descend to 2000', cleared RNAV...' I would interpret that to be descend to the platform and complete an RNAV approach and if you choose to turn it to a CDA, that would be within the clearance as issued.