With so much confusion about who to use for an international move out there, I just wanted to post my experience moving with Gentle Giant Moving Company from Boston to London. I can't tell you enough how much I would recommend someone to use them. I know that they are usually pretty expensive for local moves, but their international moving department is stellar and pricing is reasonable.
For example, hubby and I moved his musical equipment and a bunch of boxes totalling about 200 cubic feet (no furniture). For this, I was charged about $3100 and this included them coming to pack up my items for me and labelled/numbered each box, then once at their warehouse, they packed the items onto a crate and onto a shared container w/Rainer. On the UK end, they used Abels Moving. They were wonderful to deal with also. I did have to pay a bit more for them to deliver my items to a 3rd floor flat, but it was worth it since we don't have a lift in the building.
A few of our items are still packed away, but from what we've seen, nothing is broken. My husbands guitars and amps were some of the most fragile items and they are perfectly fine.
Bob Lane at Gentle Giant coordinates ALL of their international shipping/moving and is amazing. Any question I had, he answered as quickly as he could...usually within a day or so. Also, at Abels, Helen Pernold was wonderful. Again, she answered my questions I had about any of the paperwork I needed to complete on this end. They even have storage available for until you are able to have your items delivered. They'll just house the crate at their warehouse for you...for much much less than a self storage place around.