Get quotes from at least 4 international movers. Be very specific --it's a (x) bedroom or a whole (x) sized house or an (x) size storage unit. Compare & narrow to 2. If 1 is cheaper call each & say you've narrowed it down to between them & another. Whatever new deal they may offer, make sure you get it in writing in an email BEFORE agreeing. Don't rely on ANY verbal agreements/offers cuz it'll only bite you in the bum.
If you're doing all the boxing up make sure they know this. Be very specific--I'm boxing my items. You (the company) can supply (x) amount of boxes but no more. 4 is a good number 2 large 2 medium.
The movers are going to put tags on everything & log it on the manifest. They will probably wrap everything in paper. Make sure they put the tag on the OUTSIDE or write the tag number on the paper so you'll know what that lumpy brown paper wrapped blob is when it arrives. They're going to ask what's in everything you packed. You don't have to itemize list the whole content it can be --bedroom items, bathroom items, kitchen items etc. Write it on the boxes yourself as you pack. DON'T write "fragile" on anything -- double box if you must otherwise they're gonna unpack and repack it in their own boxes.
DON'T let them get lazy & write "fabric" on 30 lines on the manifest! Customs will red flag this quick as a sneeze. I had to explain that 5 boxes were fabric & the rest were my towels, blankets, & clothes. Yes technically these are made of "fabric" but there's a big difference between possibly having to pay customs import fees.
DON'T bring absolutely everything you own. Sell what you can & buy over here. Yes I know it's hard to give up the antique bedroom set you've have for years but it's HEAVY & if you go over the weight allowance in your quote, you WILL be charged the difference.
The timeframe they give is from pickup to port dump. Customs will take as long as it takes--you could get lucky & it's a couple of days just depends on the mood of the customs agent that day. A different moving company will contact you saying they're the UK side for delivery. They're going to deliver when it's convenient for them--meaning you give them specific dates when YOU'RE available & they'll see who else is in your area getting a delivery from them. You may need to bug them otherwise you'll end up being put off with excuses---squeaky wheel may get the grease but I ended up having to threaten them with a solicitor (lawyer) when they held my things hostage for 6 weeks saying they didn't have any deliveries to my area. It wasn't my fault they were 206 miles away.
This long reply may look depressing but anything bad that could happen DID happen to me. The whole traumatic episode took a total of 17 weeks from pickup to delivery because I didn't pay attention to details, didn't get everything in writing, didn't watch them writing the manifest, & finally had to become the "pushy" American.
I won't say which horrible US company I used in an open reply. But if you send me a pm I will tell you who NOT to use no matter what they promise.
Otherwise---Good Luck with your move!

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