There are always big bundles of boxes outside shopping areas. I got fuckloads off of Neal St, and because in central London the street rubbish teams collect about four times a day they're never hanging around long enough to get rained on or pissed on by a dog or whatever.
This is what I do (and I've had to move quite a few times, so I'm an old hand), but I'm one of those freaks who likes making lists so it might be a little OTT for you.
Firstly you need to pack a suitcase full of the clothes, shoes, and toiletries you'll be needing until you're moved in. Also put aside any import documents you might have to produce (I don't know if normal people have to do that, but wasters like me have to cart around reams of stuff like benefits letters, bank statements, ID, doctors letters etc etc).
My things can be split into the following categories:
books
make up and hair stuff
clothes
coats
shoes
sewing stuff
drawing stuff
bits of ornamental tat
food
plates and pans
Don't mix things up. Start using your food up now. The plates and pans should be the last things you pack, and the kettle, tea and cups should be easily accesible so you can make a cup immediately after you've moved (get your priorities right!)
Be systematic and work from room to room. Don't get bored and move on to another room half way through, or it'll be chaos.
When you're moving in, put the boxes and furniture into the rooms they're meant to be in, eg. duvet and clothes in the bedroom, kitchen stuff in the kitchen, etc.
Unpack as soon as you can - put aside the weekend after you move in and aim to be COMPLETELY unpacked by the Sunday night.
I think that coves it really.