Arriving from cruise April 24th in Southhampton, trying to figure the best way to get to Paris. Is it better to take a train to London or get a car service. Also, would I need to change train stations for the express train? Can all this be done in one day?
Yes, it can be done in a day. For instance leave Southampton at 1000, you arrive at Paris at 1651. (and runs basically hourly).
A train will always get you to London faster than a car service- the train is 1 hour 20 minutes to Waterloo + 15 minutes for the transfer to St Pancras.
A car service will take at least 2 hours, depending on traffic.
You protect the connection in London by buying the train ticket from Southampton not to London Waterloo, but to London International (which includes the tube fare, as an added extra). But the real point is that if the train into Waterloo is late that allows you to transfer to the next available Eurostar. Of course it doesn't protect you against the cruise ship docking late (due to weather, a medical issue, attending an SOS at sea, etc) or even diverting - all of which happens.