The container ship was due to arrive in Felixstowe on Saturday so I still haven't received the contents of the container. If the ship was on time, delivery should be this week.
When you receive an estimate from a moving company, the cost is based on estimated weight. Once the container is loaded. it is weighed before being shipped to a US port of departure. The cost to ship a 20' container with 3600 lbs. from my residence in Ohio to my UK residence was $5933. There is an additional cost of insurance which you must determine based on the value of goods shipped. The $5933 includes packing boxes and wrapping furniture by the movers, all cartons, paper, etc., loading the container, shipping the container, getting container through customs in the UK, shipping the container to your UK address, unloading and unpacking, disposing of wrapping paper, etc. If you use an international mover, you cannot pack your own goods if you want them insured. Because you have so little to bring, you may want to check into sharing a container with another person. An international move is not like a local or cross country move. Again, Marina at Sterling International in Louisville, KY is excellent.