We got back to Southampton at 5 am breakfast was served from 6am and we were off the ship by 6.45am and Royal Caribbean had us on our way to Heathrow even although our flight was not until mid afternoon. The first passengers left the ship at 6.30am.
This wont be a problem. Although the ship gets in early, disembarkation usually starts around 8.30-9am since it will take a while to assemble 4000 suitcases in the terminal. Have a liesurely breakfast onboard then disembark and meet your friends.
We cruised on Independence last August we arrived into Southampton at 5am and by 9.30 they had nearly everyone off the ship they give you a colour for your baggage and you follow that colours time, each colour has a time slot of about half an hour to be in the theatre waiting to disembark they call you from there but it is very good how it is all done hope this helps.