Anyone got any good recommendations? I went to Homebase and they had a pretty poor selection. I want something with lots of little dividers for all the bolts/valve caps/stem spacers etc.. i've got laying around.
halfords often have a good selection
Hate to say it but Halfrauds have a decent enough range.
my local b&q had a 2" deep case with moveable dividers in the clearance bit for £3 yesterday. You won't get much else in there though. My 'main' bike toolbox was from homebase years ago and is just what you describe.
I find it easier to get one of those plastic containers with smaller compartments in them for all those little bits and keep that inside my toolbox. That way, when you knock/bodge/tilt/drop your toolbox (and you will at some point!) all the valve caps/washers/disc rotor bolts/spacers/etc., don't go everywhere.
I've got a Halfords 'snap on' style metal one with drawers together with various dividing & holding things made to fit inside
Stanley Sortmaster is good for storing parts in- as psling says if you use the storage compartments in the lid or inside a toolbox it's probably when, not if, the box gets knocked over or left with the catches undone then lifted up, and it's a horrible feeling 
try machine mart they have stores dotted round the country plus internet
My 20 year old Snap-on style tool box from Halfords thats been up and down the road, in and out the van and car, loaded with tools, it takes 2 to pick it up, is still going strong and nothing has ever broken on it, its been a good toolbox to me. enough said.
I used to work at Homebase and have to admit the toolbox selection was poor, but they do take up a lot of space and customers always break the cheap ones. The more expensive Stanley ones are good though.
I think my longest serving toolbox is a Curver one (yes the bin folk) and it's been brilliant. I've seen lots of workmen with them and I can't ever see me breaking it despite it being plastic. I just wish it was bigger. Not sure if they still make them now.
Have a look at Machine Mart. They have some very good quality tool boxes.
I tried a few toolboxes, settle on an open tote bag for a while but still found everything ended up in a jumbled mess at the bottom, and brake fluid/shock oil soaked the bottom which isn't good as it spends half its time indoors.
Then I saw a bucket organiser bag in a horse shop, got the gf to buy it and then emptied my toolbox into it before she filled it with brushes, hoof picks and horse treats...it is perfect, decent tall pockets for all the tools, and all the bottles of fluid stand in the bucket and can't fall over and leak. You would still need a compartmentalised box for all the bobbins, though I just keep them mixed up in a couple of ziplock bags and then stuff them in the mesh pocket on the outside.