When we sailed on the Magic last September (so taking the
DCL bus to Dover rather than Southampton, but otherwise a similar situation in that we were not staying at the DCL hotel), we arrived about 10 or 15 minutes prior to our scheduled time. There was assistance right at the drop off point in front of the hotel (Doubletree by Hilton at that time for bus pick-up to go to the port; the DCL hotel was the Churchill, so the Doubletree was only used as an assembly point for those like us who booked our own hotels and only booked transfers from London to the port) who took our luggage and loaded it onboard a truck that carried the checked bags to the port. We next saw it outside our room on onboard. We kept our carry-on bags with us and were directed to a meeting room with rows of chairs set up for us to wait. After about 30 minutes, we were directed to a bus, they loaded carry-on bags into the luggage hold, we boarded and drove to the port, retrieving our carry-ons once there.