AutoBit,
These were the people I went to some years ago when furniture was mishandled. They have an arbitration service, and whilst working for their members, they also are keen to preserve their reputation.
On one of our moves, our furniture went into storage with a company based at (former) RAF Carlisle. They had this fully automated warehouse, with effects stored in ISO containers. They were very flexible approach to their business, and would happily allow additions to storage without too much fuss. Unfortunately, they lost the storage contract whilst we were abroad; First thing we knew was when we contacted them to get our effects and was told Agility had transhipped them to a company in the Midlands. Our furniture had been put in the classic wooden crates and everything seemed to be accounted for; two years later we are still saying 'what happened to, you know, that thingy that we put in storage?' I guess we'll never know - did we get rid of it or did it go into storage?
I suppose it is inevitable that there will be disruption and heartache in these moves, however the small consignments (I doubt the volumes have changed for many decades), increasingly tighter restrictions on what can be moved or stored - and added to the lack of support when moving overseas, especially if you are 'diaspora' - just seems to make the moves unnecessarily difficult.
EDITED TO ADD: for anyone moving over the next 6 months, get booked in quickly, because of the huge surge of unit moves from Germany. We had this two years ago in our previous move which was along the lines of 'where is your unit moving to?'