Get more boxes than you think, the sturdier the better. Buy a parcel tape dispenser, and don't buy cheap parcel tape, it's rubbish, get the decent stuff. It'll save you hours. Use cardboard wardrobes - you won't need to take anything off hangers.
If you can, clear out one room first, hoover it and close the door. As you pack stuff, put the boxes into that room and close the door again. It'll help keep the chaos shut away and stop you losing your mind in the run up to the move.
A couple of days before moving, pack absolutely everything from your kitchen apart from a plate and a bowl each, minimal cutlery and mugs. Live on ready meals and takeaways until you move.
Have a roll of bin bags out, you'll use them. Have one bag with bleach, one cleaning spray, washing up liquid, cleaning cloths, hoover bags if you need them, a few hand towels (good for a last minute wipe round) and tea towels. Everything else can be packed away in advance. Be ruthless.
I've never needed a skip, and have moved loads of times.
On the last morning, add tea/coffee, milk, the kettle, a loaf, butter etc to your cleaning bag, ready to take to the new house.
Good luck!