It is not so much a case that trains and coaches are full, it is that there are no actual trains and coaches running over the holiday period! The rail network is totally shut down on 25th Dec (apart from Heathrow/Gatwick Express) and almost completely shut down on 26the Dec. See here for details:
http://www.nationalrail.co.uk/times_...ndex_2009.html
I expect National Express coaches are the same. You may be able to find local buses (which you will most definitely not be able to book in advance), but only on 26th Dec - try out
http://www.traveline-northwest.co.uk I can't offer much better help - don't arrive on 25th Dec if you actually need to get anywhere else that day, and be prepared for a time consuming routing or huge expense on 26th Dec.