Are you staying in the area or moving away? The reason for the question is that outside of London prices are generally cheaper. For example, a few years ago my mother-in-law moved from London to Lincolnshire and was getting quotes from London removal firms. I got her a quote from a local firm in Lincolnshire where we lived at the time and it was £300 cheaper! Whichever way you look at it, it's two journeys. Either a full lorry going up and travelling back empty, or vice-versa.
MrsR and I are moving to Sydenham (hopefully) - not local (SE1), but still in London. We've had a quote from Monarch, in Essex somewhere. We may end up going with a van hire, rather than a removal company.
I can recommend Rocket Van Removals (http://www.rocketvan.co.uk/index.html). I've used them twice to move into and out of SE1 and they have been brilliant both times. Prices have gone up a bit from what's on the website (£60/hr for van and two men), but still worth the money.