Some thoughts on what worked, and what may have helped.

1) Take pictures before the packers start of things like books, cds, and other 'multiple' things so that should you lose a box then there's a record of what is missing, and not jsut 'err, about a shelf and a half of books, can't remember what's missing'.
2) Vanilla essence in the fridge worked a treat.
3) Clear out the garage. There's really not a lot of need for 10 UK plug socket fronts / cases in NZ.
4) Put wire cutter/strippers, screwdriver, and knife in the 'Bits Box' or other priority marked box as you need that for the set up.
5) You'll get a pile of sheets with box numbers and brief descriptions. Take a photocopy of this, and mark on it which room each box needs to go into. Ideally recopy that sheet a couple of times (A3?) and tape that up so the packing guys know where to carry all the stuff, and don't need to pause for you to give instructions for each box. Not a problems if you move out of a 3 bed 2 lounge house into a 3 bed 2 lounge house in NZ as it will all go into the same rooms, you just need to tell them what's bed 1/2/3 etc But if the layout is different, as it may well be, then this helps. I made the one list, but didn't do the photocopy for them, and so struggled to keep up with ticking the boxes off and also directing the guys into the right place.
6) Get some stubbies in the day before. Nipping out on the day to get some chilled ones may seem a 2 minute job, but come the day then it will be frantic anyway, so it's one less job to do and will be appreciated. (for the crew, not for you!)
7) Don't assume that it's glasses/china that is going to be broken. Because it's obviously fragile then you may find that's been really really well wrapped. It's the other things that may not have had the same care, so you really need to plan to either unpack, or open, then repack within the week to notify them of any faults.
8) Be realistic and expect a few things to go missing / be damaged. No, it shouldn't happen, and yes they should take care. But in the thousands if items that you have are damaged then it's less than 0.1% of the stuff they have packed, and a 99.9% success rate for most things is pretty darn good (certainly good enough for a disinfectant)
9) This week of all weeks then it's easy to put any breakages/lost things into perspective. But that stays the same all the time really.
10) You have shipping insurance, but don't just assume you need to claim on that. If you feel that there's been a failure for the movers to undertake their duty of care and deliver the service that you've paid for then communicate that to them.
11) More pragmatism. If something is chipped/scratched/bent/dented then does it matter. In some cases it will, but in others then it won't How many things have you got around the house that are 'worn'. So after a week, then you'll not notice it unless you get yourself all worked up about it. Mention it, but don't go overboard, pick and choose your battles and focus on resolving the things that are really important to you, and show that you're not expecting the impossible or trying to make up for not winning the lottery by claiming for new replacement items for every 10 year old widget that has been slightly cosmetically damaged.

So those are my thoughts and tips to myself for should there ever be a next time. Hope they help others.