We are making the big move to the uk in 2 weeks with our newborn and toddler. The biggest piece of advice (if you are looking to sell most of your things) is start now. Especially if you have a car to sell. Gumtree is quite good. We are shipping some items such as cot, bed, drawers and clothes/toys.
We have managed to live without most of our furniture for 6 weeks and like the others above, have made do for eg with our patio furniture as living furniture. We provided notice to our letting agent and have removalists arriving 4 days before departure, the cleaners arriving 3 days before and handing the keys in on the same day. This leaves us with 2 days before our flights allowing for any last minute items to address.
We are staying in a serviced apartment for our last couple of days and will then be staying with family for a few weeks once we arrive in the UK. We are fortunate though to be able to borrow cots and and a double bed from my family until our shipping arrives and we have somewhere to rent. You could always look at gumtree UK for any items to buy cheaply, some items are even offered free.
Also make check any notice requirements when cancelling bills. For eg internet provider requires 28 days.
It's certainly not cheap to move overseas so we hope not to be doing it again anytime soon!
good luck