I have cruised out of Southampton twice, 2023 and 2024. Before that, when The Magic was in Europe Disney sailed out of Dover.
The issue happened with the August 2023 cruises which were switched last minute from Horizon Terminal to Queen Elizabeth 2 Terminal. We were supposed to go from Horizon and the letter with the luggage tags said Horizon Terminal, but about 5 weeks before departure we were moved, obviously due to a scheduling issue at Southampton Port and it would have been Southampton Port Authorities that moved us, not Disney.
We were notified by email and it was well communicated online. They had shuttle buses for people who had booked parking in the wrong carpark.
Disney are not a major player in Europe and get bumped from the main terminals and port docks if there are other cruise lines who need the space. A similar thing happened at one of my 2024 ports, we were moved from the main cruise dock as another cruise line was also in port.
I am booked on my 4th
DCL cruise, my 3rd out of Southampton for August 2025. Unless you hear otherwise, Disney cruises use Horizon Terminal at Southampton.