Checker Cars is the main taxi service at Soutampton - call them and ask:
I am a bit reluctant to answer your question as I do not really know exactly how much the taxi would cost, however the airport is actually right on the City limits, so it should take no longer than about 20 minutes journey time. The M27/M271 motorway actually joins the two, and there is only one junction between them. Whether the driver would choose that route, or take the A roads, I wouldn't like to say! I would request him go the motorway route if possible, as I think the meter would be kinder to you that way, and there is less chance of him taking you on a "guide tour" of Southampton since you obviously don't know the area! The fare would not be that expensive if that is what you are worried about? If pushed I would guess at about £15. You will have to check as advised below if you are still concerned. Happy cruising.