Southampton is about 2 and a half hours drive from central London.
DCL in 2023 had transport from London Gatwick Airport and London Heathrow airport as well as a hotel in London. I would ring DCL and ask about the central London transfer. See if it is near or maybe its the same hotel that you will be in for ABD.
The DCL transfers from London to Southampton work the same as the DCL transfers in Florida. When you do online check in you put your travel details in.