Can I hire a car if I am coming into Southampton Train Station rather than the Airport?
Yes. You should be able to but weekends it may not be open you need to stick ideally to office hours Monday to Friday or Saturday morning
So I don't have to be using the airport? I am coming down to Southampton by train and visiting family so wanted to pick up the car and use it locally.
I'm coming in on Sunday.
Tomorrow is Sunday will not be possible only the airport.
I notice some of the other car hire places say I must enter flight number or cannot hire from this branch.
The flight number is not mandatory. You should be able to book without it.