Hermie,
it does make a diffenrence.
"Descend on the ILS" is an actual clearance to descend on the glidepath. This is the UK equivalent of the continental "Cleared approach"
"Continue Approach" is used by twr controllers to tell the pilot he's not cleared to land yet and making this unambiguous.
Reason for descending on the glide path has mainly to do with other traffic. At LHR there is traffic operating underneath the glidepath. (separated). To tell a pilot to descend on the ILS he will stay seperated from that traffic.