You don't have to be at the port. You hire a firm that does international moves, and they contract with a local mover on either end. So all you need to do is be there at your US home for the movers to pick up, and then again at your UK home for the movers to deliver. I even had the movers in the US pack everything for me.
If you Google international movers, you should come up with some names. I came from the east coast of the US, but used Rainier which is a west coast company. My experience was excellent, but that was back in 2003 so I have no idea if they're still good. Perhaps someone else who moved over more recently can give you a more up-to-date recommendation.