One of the biggest tips that can be given to anyone looking to move home is to be organised. Even if you aren't sure exactly when you're moving start thinking about what you can pack now, who you need to tell you are moving and making vague arrangements. If your house is anything like mine it is full of stuff that you don't touch from one week to the next, so why not start getting organised and these things packed away.
Start looking at companies and get quotes together, so you can make a decision on who you will use when the time comes. So for example, get onto Google and look for cheap movers in London and have a look at their services and costs. Make sure you ask them when they are open over the holidays and also that they'll be able to accommodate you short notice - that way you can contact them when you are ready and you are good to go!
Remember that although the actual moving process may be stressful, it will be worth it in the end. And even if your Christmas is a little disrupted it is only one day and therefore you can celebrate another time or another day in your brand new home, and what could be better than that?
If you are planning to move soon, good luck!