Southampton to London taxi

There is some small potential for stress on the timing. I've disembarked at Southampton twice. The first time I did self assist with the luggage and made it out to the taxi rank by about 8:00. The second time I picked up my luggage at the luggage hall and it was around 8:20ish. There are lots of taxis at the terminal. Any of these would absolutely love to have a fare to London which is a big money maker for them.

My worry is that even if things go exactly as planned for disembarkation (my experience is that it is usually delayed at least 50% of the time) you still have to make it to London and check in for your Eurostar train by 12:30 pm when the gate closes. They recommend arriving by 11:45 am.

I would definitely do the self assist with the luggage so that I could get off of the ship as soon as the gangway opens. Remember those elevators will be full of people all trying to do the same thing with their luggage as well. I've ended up carrying my bags down 7 decks of stairs before due to the congestion. Bring your luggage down early to avoid this problem.

You can fly Southampton to Paris.

Agree with Camborne - fly from Southampton Airport rather than the stress of backtracking to London to catch a train.