I've done it the other way round, importing a new mill from the US. I used ACC Shipping in Gravesend:
**LINK**
Going t'other way may be different but the following points may be useful:
I don't think ACC do pallets and boxes
Normally the supplier needs to provide a description and nominal value – ACC can say what they need
They will pick up from the supplier, ie, you, and take it to the docks.
A small item will be LCL (less than a container load) so ACC will combine it with other items to minimise cost by ensuring that the container is full
They organise the ship
Into the UK they looked after all the customs forms, duties and VAT – I then paid them
They organised shipping from the UK port to me – don't know if they do the same overseas
Best thing is to give them a call; I found them pretty helpful to a novice.
Andrew