I always use the Cruise Ship Schedule at the Port of Southampton
https://www.southamptonvts.co.uk/Live_Information/Shipping_Movements_and_Cruise_Ship_Schedule/Cruise_Ship_Schedule/
As for the disembark time, I have never been able to pre-select this prior to getting onboard. Only mildly annoying, but I guess I do not worry about the "getting off the ship" again bit until much later in the trip.