You might get a better airling price flying into Greensboro or Raleigh and driving to Charlotte. (This also provides the added benefit of not staying in Charlotte any longer than you have to.) The drive there would be about two (GSO) or three (RDU) hours, all on Interstate roads. I could be wrong about the prices, but there are direct flights between London-Gatwick and RDU on American Airlines.

I don't know much about the shipping, though.