From the US I would think you would have to change at either MAN or a European hub such as AMS or CDG for SOU. So why not just fly into London with more choice of carriers and much lower fares? Heathrow is your best bet. There's a direct
coach service from LHR Central Bus station to Portsmouth which would be easier than taking the train. Portsmouth is located in Hampshire, 70 miles southwest of London. To travel by train you would need to go into central London and catch Southwest Trains from Waterloo to Portsmouth. Or from Feltham (near LHR) to Clapham Junction and change there for the Portsmouth service (also Southwest Trains). The train is slightly faster and more frequent than the coach but more time consuming (and probably more expensive) because of the need to travel via Waterloo or Clapham Junction.