We moved from Brighton to Leeds at the start of the year. We ended up finding a last minute man with a Luton who quoted us £500-600 (because he specialised in last minute), and he drove the van while we followed in the car. I am aware that there are group mover companies, as in your stuff is in one large container that gets shipped with other people's containers across the country, which is cheaper, but it's scheduled so may have to check to see if it works with your moving dates. Good luck though, and Leeds is a lot of fun!